/*****************************************************************************/
/*                                                                           */
/*  Routines for Arbitrary Precision Floating-point Arithmetic               */
/*  and Fast Robust Geometric Predicates                                     */
/*  (predicates.c)                                                           */
/*                                                                           */
/*  May 18, 1996                                                             */
/*                                                                           */
/*  Placed in the public domain by                                           */
/*  Jonathan Richard Shewchuk                                                */
/*  School of Computer Science                                               */
/*  Carnegie Mellon University                                               */
/*  5000 Forbes Avenue                                                       */
/*  Pittsburgh, Pennsylvania  15213-3891                                     */
/*  jrs@cs.cmu.edu                                                           */
/*                                                                           */
/*  This file contains C implementation of algorithms for exact addition     */
/*    and multiplication of floating-point numbers, and predicates for       */
/*    robustly performing the orientation and incircle tests used in         */
/*    computational geometry.  The algorithms and underlying theory are      */
/*    described in Jonathan Richard Shewchuk.  "Adaptive Precision Floating- */
/*    Point Arithmetic and Fast Robust Geometric Predicates."  Technical     */
/*    Report CMU-CS-96-140, School of Computer Science, Carnegie Mellon      */
/*    University, Pittsburgh, Pennsylvania, May 1996.  (Submitted to         */
/*    Discrete & Computational Geometry.)                                    */
/*                                                                           */
/*  This file, the paper listed above, and other information are available   */
/*    from the Web page http://www.cs.cmu.edu/~quake/robust.html .           */
/*                                                                           */
/*****************************************************************************/

/*****************************************************************************/
/*                                                                           */
/*  Using this code:                                                         */
/*                                                                           */
/*  First, read the short or long version of the paper (from the Web page    */
/*    above).                                                                */
/*                                                                           */
/*  Be sure to call exactinit() once, before calling any of the arithmetic   */
/*    functions or geometric predicates.  Also be sure to turn on the        */
/*    optimizer when compiling this file.                                    */
/*                                                                           */
/*                                                                           */
/*  Several geometric predicates are defined.  Their parameters are all      */
/*    points.  Each point is an array of two or three floating-point         */
/*    numbers.  The geometric predicates, described in the papers, are       */
/*                                                                           */
/*    orient2d(pa, pb, pc)                                                   */
/*    orient2dfast(pa, pb, pc)                                               */
/*    orient3d(pa, pb, pc, pd)                                               */
/*    orient3dfast(pa, pb, pc, pd)                                           */
/*    incircle(pa, pb, pc, pd)                                               */
/*    incirclefast(pa, pb, pc, pd)                                           */
/*    insphere(pa, pb, pc, pd, pe)                                           */
/*    inspherefast(pa, pb, pc, pd, pe)                                       */
/*                                                                           */
/*  Those with suffix "fast" are approximate, non-robust versions.  Those    */
/*    without the suffix are adaptive precision, robust versions.  There     */
/*    are also versions with the suffices "exact" and "slow", which are      */
/*    non-adaptive, exact arithmetic versions, which I use only for timings  */
/*    in my arithmetic papers.                                               */
/*                                                                           */
/*                                                                           */
/*  An expansion is represented by an array of floating-point numbers,       */
/*    sorted from smallest to largest magnitude (possibly with interspersed  */
/*    zeros).  The length of each expansion is stored as a separate integer, */
/*    and each arithmetic function returns an integer which is the length    */
/*    of the expansion it created.                                           */
/*                                                                           */
/*  Several arithmetic functions are defined.  Their parameters are          */
/*                                                                           */
/*    e, f           Input expansions                                        */
/*    elen, flen     Lengths of input expansions (must be >= 1)              */
/*    h              Output expansion                                        */
/*    b              Input scalar                                            */
/*                                                                           */
/*  The arithmetic functions are                                             */
/*                                                                           */
/*    grow_expansion(elen, e, b, h)                                          */
/*    grow_expansion_zeroelim(elen, e, b, h)                                 */
/*    expansion_sum(elen, e, flen, f, h)                                     */
/*    expansion_sum_zeroelim1(elen, e, flen, f, h)                           */
/*    expansion_sum_zeroelim2(elen, e, flen, f, h)                           */
/*    fast_expansion_sum(elen, e, flen, f, h)                                */
/*    fast_expansion_sum_zeroelim(elen, e, flen, f, h)                       */
/*    linear_expansion_sum(elen, e, flen, f, h)                              */
/*    linear_expansion_sum_zeroelim(elen, e, flen, f, h)                     */
/*    scale_expansion(elen, e, b, h)                                         */
/*    scale_expansion_zeroelim(elen, e, b, h)                                */
/*    compress(elen, e, h)                                                   */
/*                                                                           */
/*  All of these are described in the long version of the paper; some are    */
/*    described in the short version.  All return an integer that is the     */
/*    length of h.  Those with suffix _zeroelim perform zero elimination,    */
/*    and are recommended over their counterparts.  The procedure            */
/*    fast_expansion_sum_zeroelim() (or linear_expansion_sum_zeroelim() on   */
/*    processors that do not use the round-to-even tiebreaking rule) is      */
/*    recommended over expansion_sum_zeroelim().  Each procedure has a       */
/*    little note next to it (in the code below) that tells you whether or   */
/*    not the output expansion may be the same array as one of the input     */
/*    expansions.                                                            */
/*                                                                           */
/*                                                                           */
/*  If you look around below, you'll also find macros for a bunch of         */
/*    simple unrolled arithmetic operations, and procedures for printing     */
/*    expansions (commented out because they don't work with all C           */
/*    compilers) and for generating random floating-point numbers whose      */
/*    significand bits are all random.  Most of the macros have undocumented */
/*    requirements that certain of their parameters should not be the same   */
/*    variable; for safety, better to make sure all the parameters are       */
/*    distinct variables.  Feel free to send email to jrs@cs.cmu.edu if you  */
/*    have questions.                                                        */
/*                                                                           */
/*****************************************************************************/

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#ifdef CPU86
#include <float.h>
#endif /* CPU86 */
#ifdef LINUX
#include <fpu_control.h>
#endif /* LINUX */

#include "TetGenSource.hpp"            // Defines the symbol REAL (float or double).

/* On some machines, the exact arithmetic routines might be defeated by the  */
/*   use of internal extended precision floating-point registers.  Sometimes */
/*   this problem can be fixed by defining certain values to be volatile,    */
/*   thus forcing them to be stored to memory and rounded off.  This isn't   */
/*   a great solution, though, as it slows the arithmetic down.              */
/*                                                                           */
/* To try this out, write "#define INEXACT volatile" below.  Normally,       */
/*   however, INEXACT should be defined to be nothing.  ("#define INEXACT".) */

#define INEXACT                          /* Nothing */
/* #define INEXACT volatile */

/* #define REAL double */                      /* float or double */
#define REALPRINT doubleprint
#define REALRAND doublerand
#define NARROWRAND narrowdoublerand
#define UNIFORMRAND uniformdoublerand

/* Which of the following two methods of finding the absolute values is      */
/*   fastest is compiler-dependent.  A few compilers can inline and optimize */
/*   the fabs() call; but most will incur the overhead of a function call,   */
/*   which is disastrously slow.  A faster way on IEEE machines might be to  */
/*   mask the appropriate bit, but that's difficult to do in C.              */

#define Absolute(a)  ((a) >= 0.0 ? (a) : -(a))
/* #define Absolute(a)  fabs(a) */

/* Many of the operations are broken up into two pieces, a main part that    */
/*   performs an approximate operation, and a "tail" that computes the       */
/*   roundoff error of that operation.                                       */
/*                                                                           */
/* The operations Fast_Two_Sum(), Fast_Two_Diff(), Two_Sum(), Two_Diff(),    */
/*   Split(), and Two_Product() are all implemented as described in the      */
/*   reference.  Each of these macros requires certain variables to be       */
/*   defined in the calling routine.  The variables `bvirt', `c', `abig',    */
/*   `_i', `_j', `_k', `_l', `_m', and `_n' are declared `INEXACT' because   */
/*   they store the result of an operation that may incur roundoff error.    */
/*   The input parameter `x' (or the highest numbered `x_' parameter) must   */
/*   also be declared `INEXACT'.                                             */

#define Fast_Two_Sum_Tail(a, b, x, y) \
   bvirt = x - a; \
   y = b - bvirt

#define Fast_Two_Sum(a, b, x, y) \
   x = (REAL) (a + b); \
   Fast_Two_Sum_Tail(a, b, x, y)

#define Fast_Two_Diff_Tail(a, b, x, y) \
   bvirt = a - x; \
   y = bvirt - b

#define Fast_Two_Diff(a, b, x, y) \
   x = (REAL) (a - b); \
   Fast_Two_Diff_Tail(a, b, x, y)

#define Two_Sum_Tail(a, b, x, y) \
   bvirt = (REAL) (x - a); \
   avirt = x - bvirt; \
   bround = b - bvirt; \
   around = a - avirt; \
   y = around + bround

#define Two_Sum(a, b, x, y) \
   x = (REAL) (a + b); \
   Two_Sum_Tail(a, b, x, y)

#define Two_Diff_Tail(a, b, x, y) \
   bvirt = (REAL) (a - x); \
   avirt = x + bvirt; \
   bround = bvirt - b; \
   around = a - avirt; \
   y = around + bround

#define Two_Diff(a, b, x, y) \
   x = (REAL) (a - b); \
   Two_Diff_Tail(a, b, x, y)

#define Split(a, ahi, alo) \
   c = (REAL) (splitter * a); \
   abig = (REAL) (c - a); \
   ahi = c - abig; \
   alo = a - ahi

#define Two_Product_Tail(a, b, x, y) \
   Split(a, ahi, alo); \
   Split(b, bhi, blo); \
   err1 = x - (ahi * bhi); \
   err2 = err1 - (alo * bhi); \
   err3 = err2 - (ahi * blo); \
   y = (alo * blo) - err3

#define Two_Product(a, b, x, y) \
   x = (REAL) (a * b); \
   Two_Product_Tail(a, b, x, y)

/* Two_Product_Presplit() is Two_Product() where one of the inputs has       */
/*   already been split.  Avoids redundant splitting.                        */

#define Two_Product_Presplit(a, b, bhi, blo, x, y) \
   x = (REAL) (a * b); \
   Split(a, ahi, alo); \
   err1 = x - (ahi * bhi); \
   err2 = err1 - (alo * bhi); \
   err3 = err2 - (ahi * blo); \
   y = (alo * blo) - err3

/* Two_Product_2Presplit() is Two_Product() where both of the inputs have    */
/*   already been split.  Avoids redundant splitting.                        */

#define Two_Product_2Presplit(a, ahi, alo, b, bhi, blo, x, y) \
   x = (REAL) (a * b); \
   err1 = x - (ahi * bhi); \
   err2 = err1 - (alo * bhi); \
   err3 = err2 - (ahi * blo); \
   y = (alo * blo) - err3

/* Square() can be done more quickly than Two_Product().                     */

#define Square_Tail(a, x, y) \
   Split(a, ahi, alo); \
   err1 = x - (ahi * ahi); \
   err3 = err1 - ((ahi + ahi) * alo); \
   y = (alo * alo) - err3

#define Square(a, x, y) \
   x = (REAL) (a * a); \
   Square_Tail(a, x, y)

/* Macros for summing expansions of various fixed lengths.  These are all    */
/*   unrolled versions of Expansion_Sum().                                   */

#define Two_One_Sum(a1, a0, b, x2, x1, x0) \
   Two_Sum(a0, b , _i, x0); \
   Two_Sum(a1, _i, x2, x1)

#define Two_One_Diff(a1, a0, b, x2, x1, x0) \
   Two_Diff(a0, b , _i, x0); \
   Two_Sum( a1, _i, x2, x1)

#define Two_Two_Sum(a1, a0, b1, b0, x3, x2, x1, x0) \
   Two_One_Sum(a1, a0, b0, _j, _0, x0); \
   Two_One_Sum(_j, _0, b1, x3, x2, x1)

#define Two_Two_Diff(a1, a0, b1, b0, x3, x2, x1, x0) \
   Two_One_Diff(a1, a0, b0, _j, _0, x0); \
   Two_One_Diff(_j, _0, b1, x3, x2, x1)

#define Four_One_Sum(a3, a2, a1, a0, b, x4, x3, x2, x1, x0) \
   Two_One_Sum(a1, a0, b , _j, x1, x0); \
   Two_One_Sum(a3, a2, _j, x4, x3, x2)

#define Four_Two_Sum(a3, a2, a1, a0, b1, b0, x5, x4, x3, x2, x1, x0) \
   Four_One_Sum(a3, a2, a1, a0, b0, _k, _2, _1, _0, x0); \
   Four_One_Sum(_k, _2, _1, _0, b1, x5, x4, x3, x2, x1)

#define Four_Four_Sum(a3, a2, a1, a0, b4, b3, b1, b0, x7, x6, x5, x4, x3, x2, \
   x1, x0) \
   Four_Two_Sum(a3, a2, a1, a0, b1, b0, _l, _2, _1, _0, x1, x0); \
   Four_Two_Sum(_l, _2, _1, _0, b4, b3, x7, x6, x5, x4, x3, x2)

#define Eight_One_Sum(a7, a6, a5, a4, a3, a2, a1, a0, b, x8, x7, x6, x5, x4, \
   x3, x2, x1, x0) \
   Four_One_Sum(a3, a2, a1, a0, b , _j, x3, x2, x1, x0); \
   Four_One_Sum(a7, a6, a5, a4, _j, x8, x7, x6, x5, x4)

#define Eight_Two_Sum(a7, a6, a5, a4, a3, a2, a1, a0, b1, b0, x9, x8, x7, \
   x6, x5, x4, x3, x2, x1, x0) \
   Eight_One_Sum(a7, a6, a5, a4, a3, a2, a1, a0, b0, _k, _6, _5, _4, _3, _2, \
   _1, _0, x0); \
   Eight_One_Sum(_k, _6, _5, _4, _3, _2, _1, _0, b1, x9, x8, x7, x6, x5, x4, \
   x3, x2, x1)

#define Eight_Four_Sum(a7, a6, a5, a4, a3, a2, a1, a0, b4, b3, b1, b0, x11, \
   x10, x9, x8, x7, x6, x5, x4, x3, x2, x1, x0) \
   Eight_Two_Sum(a7, a6, a5, a4, a3, a2, a1, a0, b1, b0, _l, _6, _5, _4, _3, \
   _2, _1, _0, x1, x0); \
   Eight_Two_Sum(_l, _6, _5, _4, _3, _2, _1, _0, b4, b3, x11, x10, x9, x8, \
   x7, x6, x5, x4, x3, x2)

/* Macros for multiplying expansions of various fixed lengths.               */

#define Two_One_Product(a1, a0, b, x3, x2, x1, x0) \
   Split(b, bhi, blo); \
   Two_Product_Presplit(a0, b, bhi, blo, _i, x0); \
   Two_Product_Presplit(a1, b, bhi, blo, _j, _0); \
   Two_Sum(_i, _0, _k, x1); \
   Fast_Two_Sum(_j, _k, x3, x2)

#define Four_One_Product(a3, a2, a1, a0, b, x7, x6, x5, x4, x3, x2, x1, x0) \
   Split(b, bhi, blo); \
   Two_Product_Presplit(a0, b, bhi, blo, _i, x0); \
   Two_Product_Presplit(a1, b, bhi, blo, _j, _0); \
   Two_Sum(_i, _0, _k, x1); \
   Fast_Two_Sum(_j, _k, _i, x2); \
   Two_Product_Presplit(a2, b, bhi, blo, _j, _0); \
   Two_Sum(_i, _0, _k, x3); \
   Fast_Two_Sum(_j, _k, _i, x4); \
   Two_Product_Presplit(a3, b, bhi, blo, _j, _0); \
   Two_Sum(_i, _0, _k, x5); \
   Fast_Two_Sum(_j, _k, x7, x6)

#define Two_Two_Product(a1, a0, b1, b0, x7, x6, x5, x4, x3, x2, x1, x0) \
   Split(a0, a0hi, a0lo); \
   Split(b0, bhi, blo); \
   Two_Product_2Presplit(a0, a0hi, a0lo, b0, bhi, blo, _i, x0); \
   Split(a1, a1hi, a1lo); \
   Two_Product_2Presplit(a1, a1hi, a1lo, b0, bhi, blo, _j, _0); \
   Two_Sum(_i, _0, _k, _1); \
   Fast_Two_Sum(_j, _k, _l, _2); \
   Split(b1, bhi, blo); \
   Two_Product_2Presplit(a0, a0hi, a0lo, b1, bhi, blo, _i, _0); \
   Two_Sum(_1, _0, _k, x1); \
   Two_Sum(_2, _k, _j, _1); \
   Two_Sum(_l, _j, _m, _2); \
   Two_Product_2Presplit(a1, a1hi, a1lo, b1, bhi, blo, _j, _0); \
   Two_Sum(_i, _0, _n, _0); \
   Two_Sum(_1, _0, _i, x2); \
   Two_Sum(_2, _i, _k, _1); \
   Two_Sum(_m, _k, _l, _2); \
   Two_Sum(_j, _n, _k, _0); \
   Two_Sum(_1, _0, _j, x3); \
   Two_Sum(_2, _j, _i, _1); \
   Two_Sum(_l, _i, _m, _2); \
   Two_Sum(_1, _k, _i, x4); \
   Two_Sum(_2, _i, _k, x5); \
   Two_Sum(_m, _k, x7, x6)

/* An expansion of length two can be squared more quickly than finding the   */
/*   product of two different expansions of length two, and the result is    */
/*   guaranteed to have no more than six (rather than eight) components.     */

#define Two_Square(a1, a0, x5, x4, x3, x2, x1, x0) \
   Square(a0, _j, x0); \
   _0 = a0 + a0; \
   Two_Product(a1, _0, _k, _1); \
   Two_One_Sum(_k, _1, _j, _l, _2, x1); \
   Square(a1, _j, _1); \
   Two_Two_Sum(_j, _1, _l, _2, x5, x4, x3, x2)

/* splitter = 2^ceiling(p / 2) + 1.  Used to split floats in half.           */
static REAL splitter;
static REAL epsilon;         /* = 2^(-p).  Used to estimate roundoff errors. */
/* A set of coefficients used to calculate maximum roundoff errors.          */
static REAL resulterrbound;
static REAL ccwerrboundA, ccwerrboundB, ccwerrboundC;
static REAL o3derrboundA, o3derrboundB, o3derrboundC;
static REAL iccerrboundA, iccerrboundB, iccerrboundC;
static REAL isperrboundA, isperrboundB, isperrboundC;

/*****************************************************************************/
/*                                                                           */
/*  doubleprint()   Print the bit representation of a double.                */
/*                                                                           */
/*  Useful for debugging exact arithmetic routines.                          */
/*                                                                           */
/*****************************************************************************/

/*
void doubleprint(number)
double number;
{
unsigned long long no;
unsigned long long sign, expo;
int exponent;
int i, bottomi;

no = *(unsigned long long *) &number;
sign = no & 0x8000000000000000ll;
expo = (no >> 52) & 0x7ffll;
exponent = (int) expo;
exponent = exponent - 1023;
if (sign) {
printf("-");
} else {
printf(" ");
}
if (exponent == -1023) {
printf(
"0.0000000000000000000000000000000000000000000000000000_     (   )");
} else {
printf("1.");
bottomi = -1;
for (i = 0; i < 52; i++) {
if (no & 0x0008000000000000ll) {
printf("1");
bottomi = i;
} else {
printf("0");
}
no <<= 1;
}
printf("_%d  (%d)", exponent, exponent - 1 - bottomi);
}
}
*/

/*****************************************************************************/
/*                                                                           */
/*  floatprint()   Print the bit representation of a float.                  */
/*                                                                           */
/*  Useful for debugging exact arithmetic routines.                          */
/*                                                                           */
/*****************************************************************************/

/*
void floatprint(number)
float number;
{
unsigned no;
unsigned sign, expo;
int exponent;
int i, bottomi;

no = *(unsigned *) &number;
sign = no & 0x80000000;
expo = (no >> 23) & 0xff;
exponent = (int) expo;
exponent = exponent - 127;
if (sign) {
printf("-");
} else {
printf(" ");
}
if (exponent == -127) {
printf("0.00000000000000000000000_     (   )");
} else {
printf("1.");
bottomi = -1;
for (i = 0; i < 23; i++) {
if (no & 0x00400000) {
printf("1");
bottomi = i;
} else {
printf("0");
}
no <<= 1;
}
printf("_%3d  (%3d)", exponent, exponent - 1 - bottomi);
}
}
*/

/*****************************************************************************/
/*                                                                           */
/*  expansion_print()   Print the bit representation of an expansion.        */
/*                                                                           */
/*  Useful for debugging exact arithmetic routines.                          */
/*                                                                           */
/*****************************************************************************/

/*
void expansion_print(elen, e)
int elen;
REAL *e;
{
int i;

for (i = elen - 1; i >= 0; i--) {
REALPRINT(e[i]);
if (i > 0) {
printf(" +\n");
} else {
printf("\n");
}
}
}
*/

/*****************************************************************************/
/*                                                                           */
/*  doublerand()   Generate a double with random 53-bit significand and a    */
/*                 random exponent in [0, 511].                              */
/*                                                                           */
/*****************************************************************************/

/*
double doublerand()
{
double result;
double expo;
long a, b, c;
long i;

a = random();
b = random();
c = random();
result = (double) (a - 1073741824) * 8388608.0 + (double) (b >> 8);
for (i = 512, expo = 2; i <= 131072; i *= 2, expo = expo * expo) {
if (c & i) {
result *= expo;
}
}
return result;
}
*/

/*****************************************************************************/
/*                                                                           */
/*  narrowdoublerand()   Generate a double with random 53-bit significand    */
/*                       and a random exponent in [0, 7].                    */
/*                                                                           */
/*****************************************************************************/

/*
double narrowdoublerand()
{
double result;
double expo;
long a, b, c;
long i;

a = random();
b = random();
c = random();
result = (double) (a - 1073741824) * 8388608.0 + (double) (b >> 8);
for (i = 512, expo = 2; i <= 2048; i *= 2, expo = expo * expo) {
if (c & i) {
result *= expo;
}
}
return result;
}
*/

/*****************************************************************************/
/*                                                                           */
/*  uniformdoublerand()   Generate a double with random 53-bit significand.  */
/*                                                                           */
/*****************************************************************************/

/*
double uniformdoublerand()
{
double result;
long a, b;

a = random();
b = random();
result = (double) (a - 1073741824) * 8388608.0 + (double) (b >> 8);
return result;
}
*/

/*****************************************************************************/
/*                                                                           */
/*  floatrand()   Generate a float with random 24-bit significand and a      */
/*                random exponent in [0, 63].                                */
/*                                                                           */
/*****************************************************************************/

/*
float floatrand()
{
float result;
float expo;
long a, c;
long i;

a = random();
c = random();
result = (float) ((a - 1073741824) >> 6);
for (i = 512, expo = 2; i <= 16384; i *= 2, expo = expo * expo) {
if (c & i) {
result *= expo;
}
}
return result;
}
*/

/*****************************************************************************/
/*                                                                           */
/*  narrowfloatrand()   Generate a float with random 24-bit significand and  */
/*                      a random exponent in [0, 7].                         */
/*                                                                           */
/*****************************************************************************/

/*
float narrowfloatrand()
{
float result;
float expo;
long a, c;
long i;

a = random();
c = random();
result = (float) ((a - 1073741824) >> 6);
for (i = 512, expo = 2; i <= 2048; i *= 2, expo = expo * expo) {
if (c & i) {
result *= expo;
}
}
return result;
}
*/

/*****************************************************************************/
/*                                                                           */
/*  uniformfloatrand()   Generate a float with random 24-bit significand.    */
/*                                                                           */
/*****************************************************************************/

/*
float uniformfloatrand()
{
float result;
long a;

a = random();
result = (float) ((a - 1073741824) >> 6);
return result;
}
*/

/*****************************************************************************/
/*                                                                           */
/*  exactinit()   Initialize the variables used for exact arithmetic.        */
/*                                                                           */
/*  `epsilon' is the largest power of two such that 1.0 + epsilon = 1.0 in   */
/*  floating-point arithmetic.  `epsilon' bounds the relative roundoff       */
/*  error.  It is used for floating-point error analysis.                    */
/*                                                                           */
/*  `splitter' is used to split floating-point numbers into two half-        */
/*  length significands for exact multiplication.                            */
/*                                                                           */
/*  I imagine that a highly optimizing compiler might be too smart for its   */
/*  own good, and somehow cause this routine to fail, if it pretends that    */
/*  floating-point arithmetic is too much like real arithmetic.              */
/*                                                                           */
/*  Don't change this routine unless you fully understand it.                */
/*                                                                           */
/*****************************************************************************/

REAL exactinit()
{
   REAL half;
   REAL check, lastcheck;
   int every_other;
#ifdef LINUX
   int cword;
#endif /* LINUX */

#ifdef CPU86
#ifdef SINGLE
   _control87(_PC_24, _MCW_PC); /* Set FPU control word for single precision. */
#else /* not SINGLE */
   _control87(_PC_53, _MCW_PC); /* Set FPU control word for double precision. */
#endif /* not SINGLE */
#endif /* CPU86 */
#ifdef LINUX
#ifdef SINGLE
   /*  cword = 4223; */
   cword = 4210;                 /* set FPU control word for single precision */
#else /* not SINGLE */
   /*  cword = 4735; */
   cword = 4722;                 /* set FPU control word for double precision */
#endif /* not SINGLE */
   _FPU_SETCW(cword);
#endif /* LINUX */

   every_other = 1;
   half = 0.5;
   epsilon = 1.0;
   splitter = 1.0;
   check = 1.0;
   /* Repeatedly divide `epsilon' by two until it is too small to add to    */
   /*   one without causing roundoff.  (Also check if the sum is equal to   */
   /*   the previous sum, for machines that round up instead of using exact */
   /*   rounding.  Not that this library will work on such machines anyway. */
   do {
      lastcheck = check;
      epsilon *= half;
      if (every_other) {
         splitter *= 2.0;
      }
      every_other = !every_other;
      check = 1.0 + epsilon;
   } while ((check != 1.0) && (check != lastcheck));
   splitter += 1.0;

   /* Error bounds for orientation and incircle tests. */
   resulterrbound = (3.0 + 8.0 * epsilon) * epsilon;
   ccwerrboundA = (3.0 + 16.0 * epsilon) * epsilon;
   ccwerrboundB = (2.0 + 12.0 * epsilon) * epsilon;
   ccwerrboundC = (9.0 + 64.0 * epsilon) * epsilon * epsilon;
   o3derrboundA = (7.0 + 56.0 * epsilon) * epsilon;
   o3derrboundB = (3.0 + 28.0 * epsilon) * epsilon;
   o3derrboundC = (26.0 + 288.0 * epsilon) * epsilon * epsilon;
   iccerrboundA = (10.0 + 96.0 * epsilon) * epsilon;
   iccerrboundB = (4.0 + 48.0 * epsilon) * epsilon;
   iccerrboundC = (44.0 + 576.0 * epsilon) * epsilon * epsilon;
   isperrboundA = (16.0 + 224.0 * epsilon) * epsilon;
   isperrboundB = (5.0 + 72.0 * epsilon) * epsilon;
   isperrboundC = (71.0 + 1408.0 * epsilon) * epsilon * epsilon;

   return epsilon; /* Added by H. Si 30 Juli, 2004. */
}

/*****************************************************************************/
/*                                                                           */
/*  grow_expansion()   Add a scalar to an expansion.                         */
/*                                                                           */
/*  Sets h = e + b.  See the long version of my paper for details.           */
/*                                                                           */
/*  Maintains the nonoverlapping property.  If round-to-even is used (as     */
/*  with IEEE 754), maintains the strongly nonoverlapping and nonadjacent    */
/*  properties as well.  (That is, if e has one of these properties, so      */
/*  will h.)                                                                 */
/*                                                                           */
/*****************************************************************************/

int grow_expansion(int elen, REAL *e, REAL b, REAL *h)
/* e and h can be the same. */
{
   REAL Q;
   INEXACT REAL Qnew;
   int eindex;
   REAL enow;
   INEXACT REAL bvirt;
   REAL avirt, bround, around;

   Q = b;
   for (eindex = 0; eindex < elen; eindex++) {
      enow = e[eindex];
      Two_Sum(Q, enow, Qnew, h[eindex]);
      Q = Qnew;
   }
   h[eindex] = Q;
   return eindex + 1;
}

/*****************************************************************************/
/*                                                                           */
/*  grow_expansion_zeroelim()   Add a scalar to an expansion, eliminating    */
/*                              zero components from the output expansion.   */
/*                                                                           */
/*  Sets h = e + b.  See the long version of my paper for details.           */
/*                                                                           */
/*  Maintains the nonoverlapping property.  If round-to-even is used (as     */
/*  with IEEE 754), maintains the strongly nonoverlapping and nonadjacent    */
/*  properties as well.  (That is, if e has one of these properties, so      */
/*  will h.)                                                                 */
/*                                                                           */
/*****************************************************************************/

int grow_expansion_zeroelim(int elen, REAL *e, REAL b, REAL *h)
/* e and h can be the same. */
{
   REAL Q, hh;
   INEXACT REAL Qnew;
   int eindex, hindex;
   REAL enow;
   INEXACT REAL bvirt;
   REAL avirt, bround, around;

   hindex = 0;
   Q = b;
   for (eindex = 0; eindex < elen; eindex++) {
      enow = e[eindex];
      Two_Sum(Q, enow, Qnew, hh);
      Q = Qnew;
      if (hh != 0.0) {
         h[hindex++] = hh;
      }
   }
   if ((Q != 0.0) || (hindex == 0)) {
      h[hindex++] = Q;
   }
   return hindex;
}

/*****************************************************************************/
/*                                                                           */
/*  expansion_sum()   Sum two expansions.                                    */
/*                                                                           */
/*  Sets h = e + f.  See the long version of my paper for details.           */
/*                                                                           */
/*  Maintains the nonoverlapping property.  If round-to-even is used (as     */
/*  with IEEE 754), maintains the nonadjacent property as well.  (That is,   */
/*  if e has one of these properties, so will h.)  Does NOT maintain the     */
/*  strongly nonoverlapping property.                                        */
/*                                                                           */
/*****************************************************************************/

int expansion_sum(int elen, REAL *e, int flen, REAL *f, REAL *h)
/* e and h can be the same, but f and h cannot. */
{
   REAL Q;
   INEXACT REAL Qnew;
   int findex, hindex, hlast;
   REAL hnow;
   INEXACT REAL bvirt;
   REAL avirt, bround, around;

   Q = f[0];
   for (hindex = 0; hindex < elen; hindex++) {
      hnow = e[hindex];
      Two_Sum(Q, hnow, Qnew, h[hindex]);
      Q = Qnew;
   }
   h[hindex] = Q;
   hlast = hindex;
   for (findex = 1; findex < flen; findex++) {
      Q = f[findex];
      for (hindex = findex; hindex <= hlast; hindex++) {
         hnow = h[hindex];
         Two_Sum(Q, hnow, Qnew, h[hindex]);
         Q = Qnew;
      }
      h[++hlast] = Q;
   }
   return hlast + 1;
}

/*****************************************************************************/
/*                                                                           */
/*  expansion_sum_zeroelim1()   Sum two expansions, eliminating zero         */
/*                              components from the output expansion.        */
/*                                                                           */
/*  Sets h = e + f.  See the long version of my paper for details.           */
/*                                                                           */
/*  Maintains the nonoverlapping property.  If round-to-even is used (as     */
/*  with IEEE 754), maintains the nonadjacent property as well.  (That is,   */
/*  if e has one of these properties, so will h.)  Does NOT maintain the     */
/*  strongly nonoverlapping property.                                        */
/*                                                                           */
/*****************************************************************************/

int expansion_sum_zeroelim1(int elen, REAL *e, int flen, REAL *f, REAL *h)
/* e and h can be the same, but f and h cannot. */
{
   REAL Q;
   INEXACT REAL Qnew;
   int index, findex, hindex, hlast;
   REAL hnow;
   INEXACT REAL bvirt;
   REAL avirt, bround, around;

   Q = f[0];
   for (hindex = 0; hindex < elen; hindex++) {
      hnow = e[hindex];
      Two_Sum(Q, hnow, Qnew, h[hindex]);
      Q = Qnew;
   }
   h[hindex] = Q;
   hlast = hindex;
   for (findex = 1; findex < flen; findex++) {
      Q = f[findex];
      for (hindex = findex; hindex <= hlast; hindex++) {
         hnow = h[hindex];
         Two_Sum(Q, hnow, Qnew, h[hindex]);
         Q = Qnew;
      }
      h[++hlast] = Q;
   }
   hindex = -1;
   for (index = 0; index <= hlast; index++) {
      hnow = h[index];
      if (hnow != 0.0) {
         h[++hindex] = hnow;
      }
   }
   if (hindex == -1) {
      return 1;
   } else {
      return hindex + 1;
   }
}

/*****************************************************************************/
/*                                                                           */
/*  expansion_sum_zeroelim2()   Sum two expansions, eliminating zero         */
/*                              components from the output expansion.        */
/*                                                                           */
/*  Sets h = e + f.  See the long version of my paper for details.           */
/*                                                                           */
/*  Maintains the nonoverlapping property.  If round-to-even is used (as     */
/*  with IEEE 754), maintains the nonadjacent property as well.  (That is,   */
/*  if e has one of these properties, so will h.)  Does NOT maintain the     */
/*  strongly nonoverlapping property.                                        */
/*                                                                           */
/*****************************************************************************/

int expansion_sum_zeroelim2(int elen, REAL *e, int flen, REAL *f, REAL *h)
/* e and h can be the same, but f and h cannot. */
{
   REAL Q, hh;
   INEXACT REAL Qnew;
   int eindex, findex, hindex, hlast;
   REAL enow;
   INEXACT REAL bvirt;
   REAL avirt, bround, around;

   hindex = 0;
   Q = f[0];
   for (eindex = 0; eindex < elen; eindex++) {
      enow = e[eindex];
      Two_Sum(Q, enow, Qnew, hh);
      Q = Qnew;
      if (hh != 0.0) {
         h[hindex++] = hh;
      }
   }
   h[hindex] = Q;
   hlast = hindex;
   for (findex = 1; findex < flen; findex++) {
      hindex = 0;
      Q = f[findex];
      for (eindex = 0; eindex <= hlast; eindex++) {
         enow = h[eindex];
         Two_Sum(Q, enow, Qnew, hh);
         Q = Qnew;
         if (hh != 0) {
            h[hindex++] = hh;
         }
      }
      h[hindex] = Q;
      hlast = hindex;
   }
   return hlast + 1;
}

/*****************************************************************************/
/*                                                                           */
/*  fast_expansion_sum()   Sum two expansions.                               */
/*                                                                           */
/*  Sets h = e + f.  See the long version of my paper for details.           */
/*                                                                           */
/*  If round-to-even is used (as with IEEE 754), maintains the strongly      */
/*  nonoverlapping property.  (That is, if e is strongly nonoverlapping, h   */
/*  will be also.)  Does NOT maintain the nonoverlapping or nonadjacent      */
/*  properties.                                                              */
/*                                                                           */
/*****************************************************************************/

int fast_expansion_sum(int elen, REAL *e, int flen, REAL *f, REAL *h)
/* h cannot be e or f. */
{
   REAL Q;
   INEXACT REAL Qnew;
   INEXACT REAL bvirt;
   REAL avirt, bround, around;
   int eindex, findex, hindex;
   REAL enow, fnow;

   enow = e[0];
   fnow = f[0];
   eindex = findex = 0;
   if ((fnow > enow) == (fnow > -enow)) {
      Q = enow;
      enow = e[++eindex];
   } else {
      Q = fnow;
      fnow = f[++findex];
   }
   hindex = 0;
   if ((eindex < elen) && (findex < flen)) {
      if ((fnow > enow) == (fnow > -enow)) {
         Fast_Two_Sum(enow, Q, Qnew, h[0]);
         enow = e[++eindex];
      } else {
         Fast_Two_Sum(fnow, Q, Qnew, h[0]);
         fnow = f[++findex];
      }
      Q = Qnew;
      hindex = 1;
      while ((eindex < elen) && (findex < flen)) {
         if ((fnow > enow) == (fnow > -enow)) {
            Two_Sum(Q, enow, Qnew, h[hindex]);
            enow = e[++eindex];
         } else {
            Two_Sum(Q, fnow, Qnew, h[hindex]);
            fnow = f[++findex];
         }
         Q = Qnew;
         hindex++;
      }
   }
   while (eindex < elen) {
      Two_Sum(Q, enow, Qnew, h[hindex]);
      enow = e[++eindex];
      Q = Qnew;
      hindex++;
   }
   while (findex < flen) {
      Two_Sum(Q, fnow, Qnew, h[hindex]);
      fnow = f[++findex];
      Q = Qnew;
      hindex++;
   }
   h[hindex] = Q;
   return hindex + 1;
}

/*****************************************************************************/
/*                                                                           */
/*  fast_expansion_sum_zeroelim()   Sum two expansions, eliminating zero     */
/*                                  components from the output expansion.    */
/*                                                                           */
/*  Sets h = e + f.  See the long version of my paper for details.           */
/*                                                                           */
/*  If round-to-even is used (as with IEEE 754), maintains the strongly      */
/*  nonoverlapping property.  (That is, if e is strongly nonoverlapping, h   */
/*  will be also.)  Does NOT maintain the nonoverlapping or nonadjacent      */
/*  properties.                                                              */
/*                                                                           */
/*****************************************************************************/

int fast_expansion_sum_zeroelim(int elen, REAL *e, int flen, REAL *f, REAL *h)
/* h cannot be e or f. */
{
   REAL Q;
   INEXACT REAL Qnew;
   INEXACT REAL hh;
   INEXACT REAL bvirt;
   REAL avirt, bround, around;
   int eindex, findex, hindex;
   REAL enow, fnow;

   enow = e[0];
   fnow = f[0];
   eindex = findex = 0;
   if ((fnow > enow) == (fnow > -enow)) {
      Q = enow;
      enow = e[++eindex];
   } else {
      Q = fnow;
      fnow = f[++findex];
   }
   hindex = 0;
   if ((eindex < elen) && (findex < flen)) {
      if ((fnow > enow) == (fnow > -enow)) {
         Fast_Two_Sum(enow, Q, Qnew, hh);
         enow = e[++eindex];
      } else {
         Fast_Two_Sum(fnow, Q, Qnew, hh);
         fnow = f[++findex];
      }
      Q = Qnew;
      if (hh != 0.0) {
         h[hindex++] = hh;
      }
      while ((eindex < elen) && (findex < flen)) {
         if ((fnow > enow) == (fnow > -enow)) {
            Two_Sum(Q, enow, Qnew, hh);
            enow = e[++eindex];
         } else {
            Two_Sum(Q, fnow, Qnew, hh);
            fnow = f[++findex];
         }
         Q = Qnew;
         if (hh != 0.0) {
            h[hindex++] = hh;
         }
      }
   }
   while (eindex < elen) {
      Two_Sum(Q, enow, Qnew, hh);
      enow = e[++eindex];
      Q = Qnew;
      if (hh != 0.0) {
         h[hindex++] = hh;
      }
   }
   while (findex < flen) {
      Two_Sum(Q, fnow, Qnew, hh);
      fnow = f[++findex];
      Q = Qnew;
      if (hh != 0.0) {
         h[hindex++] = hh;
      }
   }
   if ((Q != 0.0) || (hindex == 0)) {
      h[hindex++] = Q;
   }
   return hindex;
}

/*****************************************************************************/
/*                                                                           */
/*  linear_expansion_sum()   Sum two expansions.                             */
/*                                                                           */
/*  Sets h = e + f.  See either version of my paper for details.             */
/*                                                                           */
/*  Maintains the nonoverlapping property.  (That is, if e is                */
/*  nonoverlapping, h will be also.)                                         */
/*                                                                           */
/*****************************************************************************/

int linear_expansion_sum(int elen, REAL *e, int flen, REAL *f, REAL *h)
/* h cannot be e or f. */
{
   REAL Q, q;
   INEXACT REAL Qnew;
   INEXACT REAL R;
   INEXACT REAL bvirt;
   REAL avirt, bround, around;
   int eindex, findex, hindex;
   REAL enow, fnow;
   REAL g0;

   enow = e[0];
   fnow = f[0];
   eindex = findex = 0;
   if ((fnow > enow) == (fnow > -enow)) {
      g0 = enow;
      enow = e[++eindex];
   } else {
      g0 = fnow;
      fnow = f[++findex];
   }
   if ((eindex < elen) && ((findex >= flen)
      || ((fnow > enow) == (fnow > -enow)))) {
         Fast_Two_Sum(enow, g0, Qnew, q);
         enow = e[++eindex];
   } else {
      Fast_Two_Sum(fnow, g0, Qnew, q);
      fnow = f[++findex];
   }
   Q = Qnew;
   for (hindex = 0; hindex < elen + flen - 2; hindex++) {
      if ((eindex < elen) && ((findex >= flen)
         || ((fnow > enow) == (fnow > -enow)))) {
            Fast_Two_Sum(enow, q, R, h[hindex]);
            enow = e[++eindex];
      } else {
         Fast_Two_Sum(fnow, q, R, h[hindex]);
         fnow = f[++findex];
      }
      Two_Sum(Q, R, Qnew, q);
      Q = Qnew;
   }
   h[hindex] = q;
   h[hindex + 1] = Q;
   return hindex + 2;
}

/*****************************************************************************/
/*                                                                           */
/*  linear_expansion_sum_zeroelim()   Sum two expansions, eliminating zero   */
/*                                    components from the output expansion.  */
/*                                                                           */
/*  Sets h = e + f.  See either version of my paper for details.             */
/*                                                                           */
/*  Maintains the nonoverlapping property.  (That is, if e is                */
/*  nonoverlapping, h will be also.)                                         */
/*                                                                           */
/*****************************************************************************/

int linear_expansion_sum_zeroelim(int elen, REAL *e, int flen, REAL *f,
                                  REAL *h)
                                  /* h cannot be e or f. */
{
   REAL Q, q, hh;
   INEXACT REAL Qnew;
   INEXACT REAL R;
   INEXACT REAL bvirt;
   REAL avirt, bround, around;
   int eindex, findex, hindex;
   int count;
   REAL enow, fnow;
   REAL g0;

   enow = e[0];
   fnow = f[0];
   eindex = findex = 0;
   hindex = 0;
   if ((fnow > enow) == (fnow > -enow)) {
      g0 = enow;
      enow = e[++eindex];
   } else {
      g0 = fnow;
      fnow = f[++findex];
   }
   if ((eindex < elen) && ((findex >= flen)
      || ((fnow > enow) == (fnow > -enow)))) {
         Fast_Two_Sum(enow, g0, Qnew, q);
         enow = e[++eindex];
   } else {
      Fast_Two_Sum(fnow, g0, Qnew, q);
      fnow = f[++findex];
   }
   Q = Qnew;
   for (count = 2; count < elen + flen; count++) {
      if ((eindex < elen) && ((findex >= flen)
         || ((fnow > enow) == (fnow > -enow)))) {
            Fast_Two_Sum(enow, q, R, hh);
            enow = e[++eindex];
      } else {
         Fast_Two_Sum(fnow, q, R, hh);
         fnow = f[++findex];
      }
      Two_Sum(Q, R, Qnew, q);
      Q = Qnew;
      if (hh != 0) {
         h[hindex++] = hh;
      }
   }
   if (q != 0) {
      h[hindex++] = q;
   }
   if ((Q != 0.0) || (hindex == 0)) {
      h[hindex++] = Q;
   }
   return hindex;
}

/*****************************************************************************/
/*                                                                           */
/*  scale_expansion()   Multiply an expansion by a scalar.                   */
/*                                                                           */
/*  Sets h = be.  See either version of my paper for details.                */
/*                                                                           */
/*  Maintains the nonoverlapping property.  If round-to-even is used (as     */
/*  with IEEE 754), maintains the strongly nonoverlapping and nonadjacent    */
/*  properties as well.  (That is, if e has one of these properties, so      */
/*  will h.)                                                                 */
/*                                                                           */
/*****************************************************************************/

int scale_expansion(int elen, REAL *e, REAL b, REAL *h)
/* e and h cannot be the same. */
{
   INEXACT REAL Q;
   INEXACT REAL sum;
   INEXACT REAL product1;
   REAL product0;
   int eindex, hindex;
   REAL enow;
   INEXACT REAL bvirt;
   REAL avirt, bround, around;
   INEXACT REAL c;
   INEXACT REAL abig;
   REAL ahi, alo, bhi, blo;
   REAL err1, err2, err3;

   Split(b, bhi, blo);
   Two_Product_Presplit(e[0], b, bhi, blo, Q, h[0]);
   hindex = 1;
   for (eindex = 1; eindex < elen; eindex++) {
      enow = e[eindex];
      Two_Product_Presplit(enow, b, bhi, blo, product1, product0);
      Two_Sum(Q, product0, sum, h[hindex]);
      hindex++;
      Two_Sum(product1, sum, Q, h[hindex]);
      hindex++;
   }
   h[hindex] = Q;
   return elen + elen;
}

/*****************************************************************************/
/*                                                                           */
/*  scale_expansion_zeroelim()   Multiply an expansion by a scalar,          */
/*                               eliminating zero components from the        */
/*                               output expansion.                           */
/*                                                                           */
/*  Sets h = be.  See either version of my paper for details.                */
/*                                                                           */
/*  Maintains the nonoverlapping property.  If round-to-even is used (as     */
/*  with IEEE 754), maintains the strongly nonoverlapping and nonadjacent    */
/*  properties as well.  (That is, if e has one of these properties, so      */
/*  will h.)                                                                 */
/*                                                                           */
/*****************************************************************************/

int scale_expansion_zeroelim(int elen, REAL *e, REAL b, REAL *h)
/* e and h cannot be the same. */
{
   INEXACT REAL Q, sum;
   REAL hh;
   INEXACT REAL product1;
   REAL product0;
   int eindex, hindex;
   REAL enow;
   INEXACT REAL bvirt;
   REAL avirt, bround, around;
   INEXACT REAL c;
   INEXACT REAL abig;
   REAL ahi, alo, bhi, blo;
   REAL err1, err2, err3;

   Split(b, bhi, blo);
   Two_Product_Presplit(e[0], b, bhi, blo, Q, hh);
   hindex = 0;
   if (hh != 0) {
      h[hindex++] = hh;
   }
   for (eindex = 1; eindex < elen; eindex++) {
      enow = e[eindex];
      Two_Product_Presplit(enow, b, bhi, blo, product1, product0);
      Two_Sum(Q, product0, sum, hh);
      if (hh != 0) {
         h[hindex++] = hh;
      }
      Fast_Two_Sum(product1, sum, Q, hh);
      if (hh != 0) {
         h[hindex++] = hh;
      }
   }
   if ((Q != 0.0) || (hindex == 0)) {
      h[hindex++] = Q;
   }
   return hindex;
}

/*****************************************************************************/
/*                                                                           */
/*  compress()   Compress an expansion.                                      */
/*                                                                           */
/*  See the long version of my paper for details.                            */
/*                                                                           */
/*  Maintains the nonoverlapping property.  If round-to-even is used (as     */
/*  with IEEE 754), then any nonoverlapping expansion is converted to a      */
/*  nonadjacent expansion.                                                   */
/*                                                                           */
/*****************************************************************************/

int compress(int elen, REAL *e, REAL *h)
/* e and h may be the same. */
{
   REAL Q, q;
   INEXACT REAL Qnew;
   int eindex, hindex;
   INEXACT REAL bvirt;
   REAL enow, hnow;
   int top, bottom;

   bottom = elen - 1;
   Q = e[bottom];
   for (eindex = elen - 2; eindex >= 0; eindex--) {
      enow = e[eindex];
      Fast_Two_Sum(Q, enow, Qnew, q);
      if (q != 0) {
         h[bottom--] = Qnew;
         Q = q;
      } else {
         Q = Qnew;
      }
   }
   top = 0;
   for (hindex = bottom + 1; hindex < elen; hindex++) {
      hnow = h[hindex];
      Fast_Two_Sum(hnow, Q, Qnew, q);
      if (q != 0) {
         h[top++] = q;
      }
      Q = Qnew;
   }
   h[top] = Q;
   return top + 1;
}

/*****************************************************************************/
/*                                                                           */
/*  estimate()   Produce a one-word estimate of an expansion's value.        */
/*                                                                           */
/*  See either version of my paper for details.                              */
/*                                                                           */
/*****************************************************************************/

REAL estimate(int elen, REAL *e)
{
   REAL Q;
   int eindex;

   Q = e[0];
   for (eindex = 1; eindex < elen; eindex++) {
      Q += e[eindex];
   }
   return Q;
}

/*****************************************************************************/
/*                                                                           */
/*  orient2dfast()   Approximate 2D orientation test.  Nonrobust.            */
/*  orient2dexact()   Exact 2D orientation test.  Robust.                    */
/*  orient2dslow()   Another exact 2D orientation test.  Robust.             */
/*  orient2d()   Adaptive exact 2D orientation test.  Robust.                */
/*                                                                           */
/*               Return a positive value if the points pa, pb, and pc occur  */
/*               in counterclockwise order; a negative value if they occur   */
/*               in clockwise order; and zero if they are collinear.  The    */
/*               result is also a rough approximation of twice the signed    */
/*               area of the triangle defined by the three points.           */
/*                                                                           */
/*  Only the first and last routine should be used; the middle two are for   */
/*  timings.                                                                 */
/*                                                                           */
/*  The last three use exact arithmetic to ensure a correct answer.  The     */
/*  result returned is the determinant of a matrix.  In orient2d() only,     */
/*  this determinant is computed adaptively, in the sense that exact         */
/*  arithmetic is used only to the degree it is needed to ensure that the    */
/*  returned value has the correct sign.  Hence, orient2d() is usually quite */
/*  fast, but will run more slowly when the input points are collinear or    */
/*  nearly so.                                                               */
/*                                                                           */
/*****************************************************************************/

REAL orient2dfast(REAL *pa, REAL *pb, REAL *pc)
{
   REAL acx, bcx, acy, bcy;

   acx = pa[0] - pc[0];
   bcx = pb[0] - pc[0];
   acy = pa[1] - pc[1];
   bcy = pb[1] - pc[1];
   return acx * bcy - acy * bcx;
}

REAL orient2dexact(REAL *pa, REAL *pb, REAL *pc)
{
   INEXACT REAL axby1, axcy1, bxcy1, bxay1, cxay1, cxby1;
   REAL axby0, axcy0, bxcy0, bxay0, cxay0, cxby0;
   REAL aterms[4], bterms[4], cterms[4];
   INEXACT REAL aterms3, bterms3, cterms3;
   REAL v[8], w[12];
   int vlength, wlength;

   INEXACT REAL bvirt;
   REAL avirt, bround, around;
   INEXACT REAL c;
   INEXACT REAL abig;
   REAL ahi, alo, bhi, blo;
   REAL err1, err2, err3;
   INEXACT REAL _i, _j;
   REAL _0;

   Two_Product(pa[0], pb[1], axby1, axby0);
   Two_Product(pa[0], pc[1], axcy1, axcy0);
   Two_Two_Diff(axby1, axby0, axcy1, axcy0,
      aterms3, aterms[2], aterms[1], aterms[0]);
   aterms[3] = aterms3;

   Two_Product(pb[0], pc[1], bxcy1, bxcy0);
   Two_Product(pb[0], pa[1], bxay1, bxay0);
   Two_Two_Diff(bxcy1, bxcy0, bxay1, bxay0,
      bterms3, bterms[2], bterms[1], bterms[0]);
   bterms[3] = bterms3;

   Two_Product(pc[0], pa[1], cxay1, cxay0);
   Two_Product(pc[0], pb[1], cxby1, cxby0);
   Two_Two_Diff(cxay1, cxay0, cxby1, cxby0,
      cterms3, cterms[2], cterms[1], cterms[0]);
   cterms[3] = cterms3;

   vlength = fast_expansion_sum_zeroelim(4, aterms, 4, bterms, v);
   wlength = fast_expansion_sum_zeroelim(vlength, v, 4, cterms, w);

   return w[wlength - 1];
}

REAL orient2dslow(REAL *pa, REAL *pb, REAL *pc)
{
   INEXACT REAL acx, acy, bcx, bcy;
   REAL acxtail, acytail;
   REAL bcxtail, bcytail;
   REAL negate, negatetail;
   REAL axby[8], bxay[8];
   INEXACT REAL axby7, bxay7;
   REAL deter[16];
   int deterlen;

   INEXACT REAL bvirt;
   REAL avirt, bround, around;
   INEXACT REAL c;
   INEXACT REAL abig;
   REAL a0hi, a0lo, a1hi, a1lo, bhi, blo;
   REAL err1, err2, err3;
   INEXACT REAL _i, _j, _k, _l, _m, _n;
   REAL _0, _1, _2;

   Two_Diff(pa[0], pc[0], acx, acxtail);
   Two_Diff(pa[1], pc[1], acy, acytail);
   Two_Diff(pb[0], pc[0], bcx, bcxtail);
   Two_Diff(pb[1], pc[1], bcy, bcytail);

   Two_Two_Product(acx, acxtail, bcy, bcytail,
      axby7, axby[6], axby[5], axby[4],
      axby[3], axby[2], axby[1], axby[0]);
   axby[7] = axby7;
   negate = -acy;
   negatetail = -acytail;
   Two_Two_Product(bcx, bcxtail, negate, negatetail,
      bxay7, bxay[6], bxay[5], bxay[4],
      bxay[3], bxay[2], bxay[1], bxay[0]);
   bxay[7] = bxay7;

   deterlen = fast_expansion_sum_zeroelim(8, axby, 8, bxay, deter);

   return deter[deterlen - 1];
}

REAL orient2dadapt(REAL *pa, REAL *pb, REAL *pc, REAL detsum)
{
   INEXACT REAL acx, acy, bcx, bcy;
   REAL acxtail, acytail, bcxtail, bcytail;
   INEXACT REAL detleft, detright;
   REAL detlefttail, detrighttail;
   REAL det, errbound;
   REAL B[4], C1[8], C2[12], D[16];
   INEXACT REAL B3;
   int C1length, C2length, Dlength;
   REAL u[4];
   INEXACT REAL u3;
   INEXACT REAL s1, t1;
   REAL s0, t0;

   INEXACT REAL bvirt;
   REAL avirt, bround, around;
   INEXACT REAL c;
   INEXACT REAL abig;
   REAL ahi, alo, bhi, blo;
   REAL err1, err2, err3;
   INEXACT REAL _i, _j;
   REAL _0;

   acx = (REAL) (pa[0] - pc[0]);
   bcx = (REAL) (pb[0] - pc[0]);
   acy = (REAL) (pa[1] - pc[1]);
   bcy = (REAL) (pb[1] - pc[1]);

   Two_Product(acx, bcy, detleft, detlefttail);
   Two_Product(acy, bcx, detright, detrighttail);

   Two_Two_Diff(detleft, detlefttail, detright, detrighttail,
      B3, B[2], B[1], B[0]);
   B[3] = B3;

   det = estimate(4, B);
   errbound = ccwerrboundB * detsum;
   if ((det >= errbound) || (-det >= errbound)) {
      return det;
   }

   Two_Diff_Tail(pa[0], pc[0], acx, acxtail);
   Two_Diff_Tail(pb[0], pc[0], bcx, bcxtail);
   Two_Diff_Tail(pa[1], pc[1], acy, acytail);
   Two_Diff_Tail(pb[1], pc[1], bcy, bcytail);

   if ((acxtail == 0.0) && (acytail == 0.0)
      && (bcxtail == 0.0) && (bcytail == 0.0)) {
         return det;
   }

   errbound = ccwerrboundC * detsum + resulterrbound * Absolute(det);
   det += (acx * bcytail + bcy * acxtail)
      - (acy * bcxtail + bcx * acytail);
   if ((det >= errbound) || (-det >= errbound)) {
      return det;
   }

   Two_Product(acxtail, bcy, s1, s0);
   Two_Product(acytail, bcx, t1, t0);
   Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
   u[3] = u3;
   C1length = fast_expansion_sum_zeroelim(4, B, 4, u, C1);

   Two_Product(acx, bcytail, s1, s0);
   Two_Product(acy, bcxtail, t1, t0);
   Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
   u[3] = u3;
   C2length = fast_expansion_sum_zeroelim(C1length, C1, 4, u, C2);

   Two_Product(acxtail, bcytail, s1, s0);
   Two_Product(acytail, bcxtail, t1, t0);
   Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
   u[3] = u3;
   Dlength = fast_expansion_sum_zeroelim(C2length, C2, 4, u, D);

   return(D[Dlength - 1]);
}

REAL orient2d(REAL *pa, REAL *pb, REAL *pc)
{
   REAL detleft, detright, det;
   REAL detsum, errbound;

   detleft = (pa[0] - pc[0]) * (pb[1] - pc[1]);
   detright = (pa[1] - pc[1]) * (pb[0] - pc[0]);
   det = detleft - detright;

   if (detleft > 0.0) {
      if (detright <= 0.0) {
         return det;
      } else {
         detsum = detleft + detright;
      }
   } else if (detleft < 0.0) {
      if (detright >= 0.0) {
         return det;
      } else {
         detsum = -detleft - detright;
      }
   } else {
      return det;
   }

   errbound = ccwerrboundA * detsum;
   if ((det >= errbound) || (-det >= errbound)) {
      return det;
   }

   return orient2dadapt(pa, pb, pc, detsum);
}

/*****************************************************************************/
/*                                                                           */
/*  orient3dfast()   Approximate 3D orientation test.  Nonrobust.            */
/*  orient3dexact()   Exact 3D orientation test.  Robust.                    */
/*  orient3dslow()   Another exact 3D orientation test.  Robust.             */
/*  orient3d()   Adaptive exact 3D orientation test.  Robust.                */
/*                                                                           */
/*               Return a positive value if the point pd lies below the      */
/*               plane passing through pa, pb, and pc; "below" is defined so */
/*               that pa, pb, and pc appear in counterclockwise order when   */
/*               viewed from above the plane.  Returns a negative value if   */
/*               pd lies above the plane.  Returns zero if the points are    */
/*               coplanar.  The result is also a rough approximation of six  */
/*               times the signed volume of the tetrahedron defined by the   */
/*               four points.                                                */
/*                                                                           */
/*  Only the first and last routine should be used; the middle two are for   */
/*  timings.                                                                 */
/*                                                                           */
/*  The last three use exact arithmetic to ensure a correct answer.  The     */
/*  result returned is the determinant of a matrix.  In orient3d() only,     */
/*  this determinant is computed adaptively, in the sense that exact         */
/*  arithmetic is used only to the degree it is needed to ensure that the    */
/*  returned value has the correct sign.  Hence, orient3d() is usually quite */
/*  fast, but will run more slowly when the input points are coplanar or     */
/*  nearly so.                                                               */
/*                                                                           */
/*****************************************************************************/

REAL orient3dfast(REAL *pa, REAL *pb, REAL *pc, REAL *pd)
{
   REAL adx, bdx, cdx;
   REAL ady, bdy, cdy;
   REAL adz, bdz, cdz;

   adx = pa[0] - pd[0];
   bdx = pb[0] - pd[0];
   cdx = pc[0] - pd[0];
   ady = pa[1] - pd[1];
   bdy = pb[1] - pd[1];
   cdy = pc[1] - pd[1];
   adz = pa[2] - pd[2];
   bdz = pb[2] - pd[2];
   cdz = pc[2] - pd[2];

   return adx * (bdy * cdz - bdz * cdy)
      + bdx * (cdy * adz - cdz * ady)
      + cdx * (ady * bdz - adz * bdy);
}

REAL orient3dexact(REAL *pa, REAL *pb, REAL *pc, REAL *pd)
{
   INEXACT REAL axby1, bxcy1, cxdy1, dxay1, axcy1, bxdy1;
   INEXACT REAL bxay1, cxby1, dxcy1, axdy1, cxay1, dxby1;
   REAL axby0, bxcy0, cxdy0, dxay0, axcy0, bxdy0;
   REAL bxay0, cxby0, dxcy0, axdy0, cxay0, dxby0;
   REAL ab[4], bc[4], cd[4], da[4], ac[4], bd[4];
   REAL temp8[8];
   int templen;
   REAL abc[12], bcd[12], cda[12], dab[12];
   int abclen, bcdlen, cdalen, dablen;
   REAL adet[24], bdet[24], cdet[24], ddet[24];
   int alen, blen, clen, dlen;
   REAL abdet[48], cddet[48];
   int ablen, cdlen;
   REAL deter[96];
   int deterlen;
   int i;

   INEXACT REAL bvirt;
   REAL avirt, bround, around;
   INEXACT REAL c;
   INEXACT REAL abig;
   REAL ahi, alo, bhi, blo;
   REAL err1, err2, err3;
   INEXACT REAL _i, _j;
   REAL _0;

   Two_Product(pa[0], pb[1], axby1, axby0);
   Two_Product(pb[0], pa[1], bxay1, bxay0);
   Two_Two_Diff(axby1, axby0, bxay1, bxay0, ab[3], ab[2], ab[1], ab[0]);

   Two_Product(pb[0], pc[1], bxcy1, bxcy0);
   Two_Product(pc[0], pb[1], cxby1, cxby0);
   Two_Two_Diff(bxcy1, bxcy0, cxby1, cxby0, bc[3], bc[2], bc[1], bc[0]);

   Two_Product(pc[0], pd[1], cxdy1, cxdy0);
   Two_Product(pd[0], pc[1], dxcy1, dxcy0);
   Two_Two_Diff(cxdy1, cxdy0, dxcy1, dxcy0, cd[3], cd[2], cd[1], cd[0]);

   Two_Product(pd[0], pa[1], dxay1, dxay0);
   Two_Product(pa[0], pd[1], axdy1, axdy0);
   Two_Two_Diff(dxay1, dxay0, axdy1, axdy0, da[3], da[2], da[1], da[0]);

   Two_Product(pa[0], pc[1], axcy1, axcy0);
   Two_Product(pc[0], pa[1], cxay1, cxay0);
   Two_Two_Diff(axcy1, axcy0, cxay1, cxay0, ac[3], ac[2], ac[1], ac[0]);

   Two_Product(pb[0], pd[1], bxdy1, bxdy0);
   Two_Product(pd[0], pb[1], dxby1, dxby0);
   Two_Two_Diff(bxdy1, bxdy0, dxby1, dxby0, bd[3], bd[2], bd[1], bd[0]);

   templen = fast_expansion_sum_zeroelim(4, cd, 4, da, temp8);
   cdalen = fast_expansion_sum_zeroelim(templen, temp8, 4, ac, cda);
   templen = fast_expansion_sum_zeroelim(4, da, 4, ab, temp8);
   dablen = fast_expansion_sum_zeroelim(templen, temp8, 4, bd, dab);
   for (i = 0; i < 4; i++) {
      bd[i] = -bd[i];
      ac[i] = -ac[i];
   }
   templen = fast_expansion_sum_zeroelim(4, ab, 4, bc, temp8);
   abclen = fast_expansion_sum_zeroelim(templen, temp8, 4, ac, abc);
   templen = fast_expansion_sum_zeroelim(4, bc, 4, cd, temp8);
   bcdlen = fast_expansion_sum_zeroelim(templen, temp8, 4, bd, bcd);

   alen = scale_expansion_zeroelim(bcdlen, bcd, pa[2], adet);
   blen = scale_expansion_zeroelim(cdalen, cda, -pb[2], bdet);
   clen = scale_expansion_zeroelim(dablen, dab, pc[2], cdet);
   dlen = scale_expansion_zeroelim(abclen, abc, -pd[2], ddet);

   ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
   cdlen = fast_expansion_sum_zeroelim(clen, cdet, dlen, ddet, cddet);
   deterlen = fast_expansion_sum_zeroelim(ablen, abdet, cdlen, cddet, deter);

   return deter[deterlen - 1];
}

REAL orient3dslow(REAL *pa, REAL *pb, REAL *pc, REAL *pd)
{
   INEXACT REAL adx, ady, adz, bdx, bdy, bdz, cdx, cdy, cdz;
   REAL adxtail, adytail, adztail;
   REAL bdxtail, bdytail, bdztail;
   REAL cdxtail, cdytail, cdztail;
   REAL negate, negatetail;
   INEXACT REAL axby7, bxcy7, axcy7, bxay7, cxby7, cxay7;
   REAL axby[8], bxcy[8], axcy[8], bxay[8], cxby[8], cxay[8];
   REAL temp16[16], temp32[32], temp32t[32];
   int temp16len, temp32len, temp32tlen;
   REAL adet[64], bdet[64], cdet[64];
   int alen, blen, clen;
   REAL abdet[128];
   int ablen;
   REAL deter[192];
   int deterlen;

   INEXACT REAL bvirt;
   REAL avirt, bround, around;
   INEXACT REAL c;
   INEXACT REAL abig;
   REAL a0hi, a0lo, a1hi, a1lo, bhi, blo;
   REAL err1, err2, err3;
   INEXACT REAL _i, _j, _k, _l, _m, _n;
   REAL _0, _1, _2;

   Two_Diff(pa[0], pd[0], adx, adxtail);
   Two_Diff(pa[1], pd[1], ady, adytail);
   Two_Diff(pa[2], pd[2], adz, adztail);
   Two_Diff(pb[0], pd[0], bdx, bdxtail);
   Two_Diff(pb[1], pd[1], bdy, bdytail);
   Two_Diff(pb[2], pd[2], bdz, bdztail);
   Two_Diff(pc[0], pd[0], cdx, cdxtail);
   Two_Diff(pc[1], pd[1], cdy, cdytail);
   Two_Diff(pc[2], pd[2], cdz, cdztail);

   Two_Two_Product(adx, adxtail, bdy, bdytail,
      axby7, axby[6], axby[5], axby[4],
      axby[3], axby[2], axby[1], axby[0]);
   axby[7] = axby7;
   negate = -ady;
   negatetail = -adytail;
   Two_Two_Product(bdx, bdxtail, negate, negatetail,
      bxay7, bxay[6], bxay[5], bxay[4],
      bxay[3], bxay[2], bxay[1], bxay[0]);
   bxay[7] = bxay7;
   Two_Two_Product(bdx, bdxtail, cdy, cdytail,
      bxcy7, bxcy[6], bxcy[5], bxcy[4],
      bxcy[3], bxcy[2], bxcy[1], bxcy[0]);
   bxcy[7] = bxcy7;
   negate = -bdy;
   negatetail = -bdytail;
   Two_Two_Product(cdx, cdxtail, negate, negatetail,
      cxby7, cxby[6], cxby[5], cxby[4],
      cxby[3], cxby[2], cxby[1], cxby[0]);
   cxby[7] = cxby7;
   Two_Two_Product(cdx, cdxtail, ady, adytail,
      cxay7, cxay[6], cxay[5], cxay[4],
      cxay[3], cxay[2], cxay[1], cxay[0]);
   cxay[7] = cxay7;
   negate = -cdy;
   negatetail = -cdytail;
   Two_Two_Product(adx, adxtail, negate, negatetail,
      axcy7, axcy[6], axcy[5], axcy[4],
      axcy[3], axcy[2], axcy[1], axcy[0]);
   axcy[7] = axcy7;

   temp16len = fast_expansion_sum_zeroelim(8, bxcy, 8, cxby, temp16);
   temp32len = scale_expansion_zeroelim(temp16len, temp16, adz, temp32);
   temp32tlen = scale_expansion_zeroelim(temp16len, temp16, adztail, temp32t);
   alen = fast_expansion_sum_zeroelim(temp32len, temp32, temp32tlen, temp32t,
      adet);

   temp16len = fast_expansion_sum_zeroelim(8, cxay, 8, axcy, temp16);
   temp32len = scale_expansion_zeroelim(temp16len, temp16, bdz, temp32);
   temp32tlen = scale_expansion_zeroelim(temp16len, temp16, bdztail, temp32t);
   blen = fast_expansion_sum_zeroelim(temp32len, temp32, temp32tlen, temp32t,
      bdet);

   temp16len = fast_expansion_sum_zeroelim(8, axby, 8, bxay, temp16);
   temp32len = scale_expansion_zeroelim(temp16len, temp16, cdz, temp32);
   temp32tlen = scale_expansion_zeroelim(temp16len, temp16, cdztail, temp32t);
   clen = fast_expansion_sum_zeroelim(temp32len, temp32, temp32tlen, temp32t,
      cdet);

   ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
   deterlen = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, deter);

   return deter[deterlen - 1];
}

REAL orient3dadapt(REAL *pa, REAL *pb, REAL *pc, REAL *pd, REAL permanent)
{
   INEXACT REAL adx, bdx, cdx, ady, bdy, cdy, adz, bdz, cdz;
   REAL det, errbound;

   INEXACT REAL bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1;
   REAL bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0;
   REAL bc[4], ca[4], ab[4];
   INEXACT REAL bc3, ca3, ab3;
   REAL adet[8], bdet[8], cdet[8];
   int alen, blen, clen;
   REAL abdet[16];
   int ablen;
   REAL *finnow, *finother, *finswap;
   REAL fin1[192], fin2[192];
   int finlength;

   ////////////////////////////////////////////////////////
   // To avoid uninitialized warnings reported by valgrind.
   int i;
   for (i = 0; i < 8; i++) {
      adet[i] = bdet[i] = cdet[i] = 0.0;
   }
   for (i = 0; i < 16; i++) {
      abdet[i] = 0.0;
   }
   ////////////////////////////////////////////////////////

   REAL adxtail, bdxtail, cdxtail;
   REAL adytail, bdytail, cdytail;
   REAL adztail, bdztail, cdztail;
   INEXACT REAL at_blarge, at_clarge;
   INEXACT REAL bt_clarge, bt_alarge;
   INEXACT REAL ct_alarge, ct_blarge;
   REAL at_b[4], at_c[4], bt_c[4], bt_a[4], ct_a[4], ct_b[4];
   int at_blen, at_clen, bt_clen, bt_alen, ct_alen, ct_blen;
   INEXACT REAL bdxt_cdy1, cdxt_bdy1, cdxt_ady1;
   INEXACT REAL adxt_cdy1, adxt_bdy1, bdxt_ady1;
   REAL bdxt_cdy0, cdxt_bdy0, cdxt_ady0;
   REAL adxt_cdy0, adxt_bdy0, bdxt_ady0;
   INEXACT REAL bdyt_cdx1, cdyt_bdx1, cdyt_adx1;
   INEXACT REAL adyt_cdx1, adyt_bdx1, bdyt_adx1;
   REAL bdyt_cdx0, cdyt_bdx0, cdyt_adx0;
   REAL adyt_cdx0, adyt_bdx0, bdyt_adx0;
   REAL bct[8], cat[8], abt[8];
   int bctlen, catlen, abtlen;
   INEXACT REAL bdxt_cdyt1, cdxt_bdyt1, cdxt_adyt1;
   INEXACT REAL adxt_cdyt1, adxt_bdyt1, bdxt_adyt1;
   REAL bdxt_cdyt0, cdxt_bdyt0, cdxt_adyt0;
   REAL adxt_cdyt0, adxt_bdyt0, bdxt_adyt0;
   REAL u[4], v[12], w[16];
   INEXACT REAL u3;
   int vlength, wlength;
   REAL negate;

   INEXACT REAL bvirt;
   REAL avirt, bround, around;
   INEXACT REAL c;
   INEXACT REAL abig;
   REAL ahi, alo, bhi, blo;
   REAL err1, err2, err3;
   INEXACT REAL _i, _j, _k;
   REAL _0;

   adx = (REAL) (pa[0] - pd[0]);
   bdx = (REAL) (pb[0] - pd[0]);
   cdx = (REAL) (pc[0] - pd[0]);
   ady = (REAL) (pa[1] - pd[1]);
   bdy = (REAL) (pb[1] - pd[1]);
   cdy = (REAL) (pc[1] - pd[1]);
   adz = (REAL) (pa[2] - pd[2]);
   bdz = (REAL) (pb[2] - pd[2]);
   cdz = (REAL) (pc[2] - pd[2]);

   Two_Product(bdx, cdy, bdxcdy1, bdxcdy0);
   Two_Product(cdx, bdy, cdxbdy1, cdxbdy0);
   Two_Two_Diff(bdxcdy1, bdxcdy0, cdxbdy1, cdxbdy0, bc3, bc[2], bc[1], bc[0]);
   bc[3] = bc3;
   alen = scale_expansion_zeroelim(4, bc, adz, adet);

   Two_Product(cdx, ady, cdxady1, cdxady0);
   Two_Product(adx, cdy, adxcdy1, adxcdy0);
   Two_Two_Diff(cdxady1, cdxady0, adxcdy1, adxcdy0, ca3, ca[2], ca[1], ca[0]);
   ca[3] = ca3;
   blen = scale_expansion_zeroelim(4, ca, bdz, bdet);

   Two_Product(adx, bdy, adxbdy1, adxbdy0);
   Two_Product(bdx, ady, bdxady1, bdxady0);
   Two_Two_Diff(adxbdy1, adxbdy0, bdxady1, bdxady0, ab3, ab[2], ab[1], ab[0]);
   ab[3] = ab3;
   clen = scale_expansion_zeroelim(4, ab, cdz, cdet);

   ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
   finlength = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, fin1);

   det = estimate(finlength, fin1);
   errbound = o3derrboundB * permanent;
   if ((det >= errbound) || (-det >= errbound)) {
      return det;
   }

   Two_Diff_Tail(pa[0], pd[0], adx, adxtail);
   Two_Diff_Tail(pb[0], pd[0], bdx, bdxtail);
   Two_Diff_Tail(pc[0], pd[0], cdx, cdxtail);
   Two_Diff_Tail(pa[1], pd[1], ady, adytail);
   Two_Diff_Tail(pb[1], pd[1], bdy, bdytail);
   Two_Diff_Tail(pc[1], pd[1], cdy, cdytail);
   Two_Diff_Tail(pa[2], pd[2], adz, adztail);
   Two_Diff_Tail(pb[2], pd[2], bdz, bdztail);
   Two_Diff_Tail(pc[2], pd[2], cdz, cdztail);

   if ((adxtail == 0.0) && (bdxtail == 0.0) && (cdxtail == 0.0)
      && (adytail == 0.0) && (bdytail == 0.0) && (cdytail == 0.0)
      && (adztail == 0.0) && (bdztail == 0.0) && (cdztail == 0.0)) {
         return det;
   }

   errbound = o3derrboundC * permanent + resulterrbound * Absolute(det);
   det += (adz * ((bdx * cdytail + cdy * bdxtail)
      - (bdy * cdxtail + cdx * bdytail))
      + adztail * (bdx * cdy - bdy * cdx))
      + (bdz * ((cdx * adytail + ady * cdxtail)
      - (cdy * adxtail + adx * cdytail))
      + bdztail * (cdx * ady - cdy * adx))
      + (cdz * ((adx * bdytail + bdy * adxtail)
      - (ady * bdxtail + bdx * adytail))
      + cdztail * (adx * bdy - ady * bdx));
   if ((det >= errbound) || (-det >= errbound)) {
      return det;
   }

   finnow = fin1;
   finother = fin2;

   if (adxtail == 0.0) {
      if (adytail == 0.0) {
         at_b[0] = 0.0;
         at_blen = 1;
         at_c[0] = 0.0;
         at_clen = 1;
      } else {
         negate = -adytail;
         Two_Product(negate, bdx, at_blarge, at_b[0]);
         at_b[1] = at_blarge;
         at_blen = 2;
         Two_Product(adytail, cdx, at_clarge, at_c[0]);
         at_c[1] = at_clarge;
         at_clen = 2;
      }
   } else {
      if (adytail == 0.0) {
         Two_Product(adxtail, bdy, at_blarge, at_b[0]);
         at_b[1] = at_blarge;
         at_blen = 2;
         negate = -adxtail;
         Two_Product(negate, cdy, at_clarge, at_c[0]);
         at_c[1] = at_clarge;
         at_clen = 2;
      } else {
         Two_Product(adxtail, bdy, adxt_bdy1, adxt_bdy0);
         Two_Product(adytail, bdx, adyt_bdx1, adyt_bdx0);
         Two_Two_Diff(adxt_bdy1, adxt_bdy0, adyt_bdx1, adyt_bdx0,
            at_blarge, at_b[2], at_b[1], at_b[0]);
         at_b[3] = at_blarge;
         at_blen = 4;
         Two_Product(adytail, cdx, adyt_cdx1, adyt_cdx0);
         Two_Product(adxtail, cdy, adxt_cdy1, adxt_cdy0);
         Two_Two_Diff(adyt_cdx1, adyt_cdx0, adxt_cdy1, adxt_cdy0,
            at_clarge, at_c[2], at_c[1], at_c[0]);
         at_c[3] = at_clarge;
         at_clen = 4;
      }
   }
   if (bdxtail == 0.0) {
      if (bdytail == 0.0) {
         bt_c[0] = 0.0;
         bt_clen = 1;
         bt_a[0] = 0.0;
         bt_alen = 1;
      } else {
         negate = -bdytail;
         Two_Product(negate, cdx, bt_clarge, bt_c[0]);
         bt_c[1] = bt_clarge;
         bt_clen = 2;
         Two_Product(bdytail, adx, bt_alarge, bt_a[0]);
         bt_a[1] = bt_alarge;
         bt_alen = 2;
      }
   } else {
      if (bdytail == 0.0) {
         Two_Product(bdxtail, cdy, bt_clarge, bt_c[0]);
         bt_c[1] = bt_clarge;
         bt_clen = 2;
         negate = -bdxtail;
         Two_Product(negate, ady, bt_alarge, bt_a[0]);
         bt_a[1] = bt_alarge;
         bt_alen = 2;
      } else {
         Two_Product(bdxtail, cdy, bdxt_cdy1, bdxt_cdy0);
         Two_Product(bdytail, cdx, bdyt_cdx1, bdyt_cdx0);
         Two_Two_Diff(bdxt_cdy1, bdxt_cdy0, bdyt_cdx1, bdyt_cdx0,
            bt_clarge, bt_c[2], bt_c[1], bt_c[0]);
         bt_c[3] = bt_clarge;
         bt_clen = 4;
         Two_Product(bdytail, adx, bdyt_adx1, bdyt_adx0);
         Two_Product(bdxtail, ady, bdxt_ady1, bdxt_ady0);
         Two_Two_Diff(bdyt_adx1, bdyt_adx0, bdxt_ady1, bdxt_ady0,
            bt_alarge, bt_a[2], bt_a[1], bt_a[0]);
         bt_a[3] = bt_alarge;
         bt_alen = 4;
      }
   }
   if (cdxtail == 0.0) {
      if (cdytail == 0.0) {
         ct_a[0] = 0.0;
         ct_alen = 1;
         ct_b[0] = 0.0;
         ct_blen = 1;
      } else {
         negate = -cdytail;
         Two_Product(negate, adx, ct_alarge, ct_a[0]);
         ct_a[1] = ct_alarge;
         ct_alen = 2;
         Two_Product(cdytail, bdx, ct_blarge, ct_b[0]);
         ct_b[1] = ct_blarge;
         ct_blen = 2;
      }
   } else {
      if (cdytail == 0.0) {
         Two_Product(cdxtail, ady, ct_alarge, ct_a[0]);
         ct_a[1] = ct_alarge;
         ct_alen = 2;
         negate = -cdxtail;
         Two_Product(negate, bdy, ct_blarge, ct_b[0]);
         ct_b[1] = ct_blarge;
         ct_blen = 2;
      } else {
         Two_Product(cdxtail, ady, cdxt_ady1, cdxt_ady0);
         Two_Product(cdytail, adx, cdyt_adx1, cdyt_adx0);
         Two_Two_Diff(cdxt_ady1, cdxt_ady0, cdyt_adx1, cdyt_adx0,
            ct_alarge, ct_a[2], ct_a[1], ct_a[0]);
         ct_a[3] = ct_alarge;
         ct_alen = 4;
         Two_Product(cdytail, bdx, cdyt_bdx1, cdyt_bdx0);
         Two_Product(cdxtail, bdy, cdxt_bdy1, cdxt_bdy0);
         Two_Two_Diff(cdyt_bdx1, cdyt_bdx0, cdxt_bdy1, cdxt_bdy0,
            ct_blarge, ct_b[2], ct_b[1], ct_b[0]);
         ct_b[3] = ct_blarge;
         ct_blen = 4;
      }
   }

   bctlen = fast_expansion_sum_zeroelim(bt_clen, bt_c, ct_blen, ct_b, bct);
   wlength = scale_expansion_zeroelim(bctlen, bct, adz, w);
   finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
      finother);
   finswap = finnow; finnow = finother; finother = finswap;

   catlen = fast_expansion_sum_zeroelim(ct_alen, ct_a, at_clen, at_c, cat);
   wlength = scale_expansion_zeroelim(catlen, cat, bdz, w);
   finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
      finother);
   finswap = finnow; finnow = finother; finother = finswap;

   abtlen = fast_expansion_sum_zeroelim(at_blen, at_b, bt_alen, bt_a, abt);
   wlength = scale_expansion_zeroelim(abtlen, abt, cdz, w);
   finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
      finother);
   finswap = finnow; finnow = finother; finother = finswap;

   if (adztail != 0.0) {
      vlength = scale_expansion_zeroelim(4, bc, adztail, v);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v,
         finother);
      finswap = finnow; finnow = finother; finother = finswap;
   }
   if (bdztail != 0.0) {
      vlength = scale_expansion_zeroelim(4, ca, bdztail, v);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v,
         finother);
      finswap = finnow; finnow = finother; finother = finswap;
   }
   if (cdztail != 0.0) {
      vlength = scale_expansion_zeroelim(4, ab, cdztail, v);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v,
         finother);
      finswap = finnow; finnow = finother; finother = finswap;
   }

   if (adxtail != 0.0) {
      if (bdytail != 0.0) {
         Two_Product(adxtail, bdytail, adxt_bdyt1, adxt_bdyt0);
         Two_One_Product(adxt_bdyt1, adxt_bdyt0, cdz, u3, u[2], u[1], u[0]);
         u[3] = u3;
         finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
            finother);
         finswap = finnow; finnow = finother; finother = finswap;
         if (cdztail != 0.0) {
            Two_One_Product(adxt_bdyt1, adxt_bdyt0, cdztail, u3, u[2], u[1], u[0]);
            u[3] = u3;
            finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
               finother);
            finswap = finnow; finnow = finother; finother = finswap;
         }
      }
      if (cdytail != 0.0) {
         negate = -adxtail;
         Two_Product(negate, cdytail, adxt_cdyt1, adxt_cdyt0);
         Two_One_Product(adxt_cdyt1, adxt_cdyt0, bdz, u3, u[2], u[1], u[0]);
         u[3] = u3;
         finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
            finother);
         finswap = finnow; finnow = finother; finother = finswap;
         if (bdztail != 0.0) {
            Two_One_Product(adxt_cdyt1, adxt_cdyt0, bdztail, u3, u[2], u[1], u[0]);
            u[3] = u3;
            finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
               finother);
            finswap = finnow; finnow = finother; finother = finswap;
         }
      }
   }
   if (bdxtail != 0.0) {
      if (cdytail != 0.0) {
         Two_Product(bdxtail, cdytail, bdxt_cdyt1, bdxt_cdyt0);
         Two_One_Product(bdxt_cdyt1, bdxt_cdyt0, adz, u3, u[2], u[1], u[0]);
         u[3] = u3;
         finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
            finother);
         finswap = finnow; finnow = finother; finother = finswap;
         if (adztail != 0.0) {
            Two_One_Product(bdxt_cdyt1, bdxt_cdyt0, adztail, u3, u[2], u[1], u[0]);
            u[3] = u3;
            finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
               finother);
            finswap = finnow; finnow = finother; finother = finswap;
         }
      }
      if (adytail != 0.0) {
         negate = -bdxtail;
         Two_Product(negate, adytail, bdxt_adyt1, bdxt_adyt0);
         Two_One_Product(bdxt_adyt1, bdxt_adyt0, cdz, u3, u[2], u[1], u[0]);
         u[3] = u3;
         finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
            finother);
         finswap = finnow; finnow = finother; finother = finswap;
         if (cdztail != 0.0) {
            Two_One_Product(bdxt_adyt1, bdxt_adyt0, cdztail, u3, u[2], u[1], u[0]);
            u[3] = u3;
            finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
               finother);
            finswap = finnow; finnow = finother; finother = finswap;
         }
      }
   }
   if (cdxtail != 0.0) {
      if (adytail != 0.0) {
         Two_Product(cdxtail, adytail, cdxt_adyt1, cdxt_adyt0);
         Two_One_Product(cdxt_adyt1, cdxt_adyt0, bdz, u3, u[2], u[1], u[0]);
         u[3] = u3;
         finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
            finother);
         finswap = finnow; finnow = finother; finother = finswap;
         if (bdztail != 0.0) {
            Two_One_Product(cdxt_adyt1, cdxt_adyt0, bdztail, u3, u[2], u[1], u[0]);
            u[3] = u3;
            finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
               finother);
            finswap = finnow; finnow = finother; finother = finswap;
         }
      }
      if (bdytail != 0.0) {
         negate = -cdxtail;
         Two_Product(negate, bdytail, cdxt_bdyt1, cdxt_bdyt0);
         Two_One_Product(cdxt_bdyt1, cdxt_bdyt0, adz, u3, u[2], u[1], u[0]);
         u[3] = u3;
         finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
            finother);
         finswap = finnow; finnow = finother; finother = finswap;
         if (adztail != 0.0) {
            Two_One_Product(cdxt_bdyt1, cdxt_bdyt0, adztail, u3, u[2], u[1], u[0]);
            u[3] = u3;
            finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
               finother);
            finswap = finnow; finnow = finother; finother = finswap;
         }
      }
   }

   if (adztail != 0.0) {
      wlength = scale_expansion_zeroelim(bctlen, bct, adztail, w);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
         finother);
      finswap = finnow; finnow = finother; finother = finswap;
   }
   if (bdztail != 0.0) {
      wlength = scale_expansion_zeroelim(catlen, cat, bdztail, w);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
         finother);
      finswap = finnow; finnow = finother; finother = finswap;
   }
   if (cdztail != 0.0) {
      wlength = scale_expansion_zeroelim(abtlen, abt, cdztail, w);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
         finother);
      finswap = finnow; finnow = finother; finother = finswap;
   }

   return finnow[finlength - 1];
}

REAL orient3d(REAL *pa, REAL *pb, REAL *pc, REAL *pd)
{
   REAL adx, bdx, cdx, ady, bdy, cdy, adz, bdz, cdz;
   REAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady;
   REAL det;
   REAL permanent, errbound;

   adx = pa[0] - pd[0];
   bdx = pb[0] - pd[0];
   cdx = pc[0] - pd[0];
   ady = pa[1] - pd[1];
   bdy = pb[1] - pd[1];
   cdy = pc[1] - pd[1];
   adz = pa[2] - pd[2];
   bdz = pb[2] - pd[2];
   cdz = pc[2] - pd[2];

   bdxcdy = bdx * cdy;
   cdxbdy = cdx * bdy;

   cdxady = cdx * ady;
   adxcdy = adx * cdy;

   adxbdy = adx * bdy;
   bdxady = bdx * ady;

   det = adz * (bdxcdy - cdxbdy) 
      + bdz * (cdxady - adxcdy)
      + cdz * (adxbdy - bdxady);

   permanent = (Absolute(bdxcdy) + Absolute(cdxbdy)) * Absolute(adz)
      + (Absolute(cdxady) + Absolute(adxcdy)) * Absolute(bdz)
      + (Absolute(adxbdy) + Absolute(bdxady)) * Absolute(cdz);
   errbound = o3derrboundA * permanent;
   if ((det > errbound) || (-det > errbound)) {
      return det;
   }

   return orient3dadapt(pa, pb, pc, pd, permanent);
}

/*****************************************************************************/
/*                                                                           */
/*  incirclefast()   Approximate 2D incircle test.  Nonrobust.               */
/*  incircleexact()   Exact 2D incircle test.  Robust.                       */
/*  incircleslow()   Another exact 2D incircle test.  Robust.                */
/*  incircle()   Adaptive exact 2D incircle test.  Robust.                   */
/*                                                                           */
/*               Return a positive value if the point pd lies inside the     */
/*               circle passing through pa, pb, and pc; a negative value if  */
/*               it lies outside; and zero if the four points are cocircular.*/
/*               The points pa, pb, and pc must be in counterclockwise       */
/*               order, or the sign of the result will be reversed.          */
/*                                                                           */
/*  Only the first and last routine should be used; the middle two are for   */
/*  timings.                                                                 */
/*                                                                           */
/*  The last three use exact arithmetic to ensure a correct answer.  The     */
/*  result returned is the determinant of a matrix.  In incircle() only,     */
/*  this determinant is computed adaptively, in the sense that exact         */
/*  arithmetic is used only to the degree it is needed to ensure that the    */
/*  returned value has the correct sign.  Hence, incircle() is usually quite */
/*  fast, but will run more slowly when the input points are cocircular or   */
/*  nearly so.                                                               */
/*                                                                           */
/*****************************************************************************/

REAL incirclefast(REAL *pa, REAL *pb, REAL *pc, REAL *pd)
{
   REAL adx, ady, bdx, bdy, cdx, cdy;
   REAL abdet, bcdet, cadet;
   REAL alift, blift, clift;

   adx = pa[0] - pd[0];
   ady = pa[1] - pd[1];
   bdx = pb[0] - pd[0];
   bdy = pb[1] - pd[1];
   cdx = pc[0] - pd[0];
   cdy = pc[1] - pd[1];

   abdet = adx * bdy - bdx * ady;
   bcdet = bdx * cdy - cdx * bdy;
   cadet = cdx * ady - adx * cdy;
   alift = adx * adx + ady * ady;
   blift = bdx * bdx + bdy * bdy;
   clift = cdx * cdx + cdy * cdy;

   return alift * bcdet + blift * cadet + clift * abdet;
}

REAL incircleexact(REAL *pa, REAL *pb, REAL *pc, REAL *pd)
{
   INEXACT REAL axby1, bxcy1, cxdy1, dxay1, axcy1, bxdy1;
   INEXACT REAL bxay1, cxby1, dxcy1, axdy1, cxay1, dxby1;
   REAL axby0, bxcy0, cxdy0, dxay0, axcy0, bxdy0;
   REAL bxay0, cxby0, dxcy0, axdy0, cxay0, dxby0;
   REAL ab[4], bc[4], cd[4], da[4], ac[4], bd[4];
   REAL temp8[8];
   int templen;
   REAL abc[12], bcd[12], cda[12], dab[12];
   int abclen, bcdlen, cdalen, dablen;
   REAL det24x[24], det24y[24], det48x[48], det48y[48];
   int xlen, ylen;
   REAL adet[96], bdet[96], cdet[96], ddet[96];
   int alen, blen, clen, dlen;
   REAL abdet[192], cddet[192];
   int ablen, cdlen;
   REAL deter[384];
   int deterlen;
   int i;

   INEXACT REAL bvirt;
   REAL avirt, bround, around;
   INEXACT REAL c;
   INEXACT REAL abig;
   REAL ahi, alo, bhi, blo;
   REAL err1, err2, err3;
   INEXACT REAL _i, _j;
   REAL _0;

   Two_Product(pa[0], pb[1], axby1, axby0);
   Two_Product(pb[0], pa[1], bxay1, bxay0);
   Two_Two_Diff(axby1, axby0, bxay1, bxay0, ab[3], ab[2], ab[1], ab[0]);

   Two_Product(pb[0], pc[1], bxcy1, bxcy0);
   Two_Product(pc[0], pb[1], cxby1, cxby0);
   Two_Two_Diff(bxcy1, bxcy0, cxby1, cxby0, bc[3], bc[2], bc[1], bc[0]);

   Two_Product(pc[0], pd[1], cxdy1, cxdy0);
   Two_Product(pd[0], pc[1], dxcy1, dxcy0);
   Two_Two_Diff(cxdy1, cxdy0, dxcy1, dxcy0, cd[3], cd[2], cd[1], cd[0]);

   Two_Product(pd[0], pa[1], dxay1, dxay0);
   Two_Product(pa[0], pd[1], axdy1, axdy0);
   Two_Two_Diff(dxay1, dxay0, axdy1, axdy0, da[3], da[2], da[1], da[0]);

   Two_Product(pa[0], pc[1], axcy1, axcy0);
   Two_Product(pc[0], pa[1], cxay1, cxay0);
   Two_Two_Diff(axcy1, axcy0, cxay1, cxay0, ac[3], ac[2], ac[1], ac[0]);

   Two_Product(pb[0], pd[1], bxdy1, bxdy0);
   Two_Product(pd[0], pb[1], dxby1, dxby0);
   Two_Two_Diff(bxdy1, bxdy0, dxby1, dxby0, bd[3], bd[2], bd[1], bd[0]);

   templen = fast_expansion_sum_zeroelim(4, cd, 4, da, temp8);
   cdalen = fast_expansion_sum_zeroelim(templen, temp8, 4, ac, cda);
   templen = fast_expansion_sum_zeroelim(4, da, 4, ab, temp8);
   dablen = fast_expansion_sum_zeroelim(templen, temp8, 4, bd, dab);
   for (i = 0; i < 4; i++) {
      bd[i] = -bd[i];
      ac[i] = -ac[i];
   }
   templen = fast_expansion_sum_zeroelim(4, ab, 4, bc, temp8);
   abclen = fast_expansion_sum_zeroelim(templen, temp8, 4, ac, abc);
   templen = fast_expansion_sum_zeroelim(4, bc, 4, cd, temp8);
   bcdlen = fast_expansion_sum_zeroelim(templen, temp8, 4, bd, bcd);

   xlen = scale_expansion_zeroelim(bcdlen, bcd, pa[0], det24x);
   xlen = scale_expansion_zeroelim(xlen, det24x, pa[0], det48x);
   ylen = scale_expansion_zeroelim(bcdlen, bcd, pa[1], det24y);
   ylen = scale_expansion_zeroelim(ylen, det24y, pa[1], det48y);
   alen = fast_expansion_sum_zeroelim(xlen, det48x, ylen, det48y, adet);

   xlen = scale_expansion_zeroelim(cdalen, cda, pb[0], det24x);
   xlen = scale_expansion_zeroelim(xlen, det24x, -pb[0], det48x);
   ylen = scale_expansion_zeroelim(cdalen, cda, pb[1], det24y);
   ylen = scale_expansion_zeroelim(ylen, det24y, -pb[1], det48y);
   blen = fast_expansion_sum_zeroelim(xlen, det48x, ylen, det48y, bdet);

   xlen = scale_expansion_zeroelim(dablen, dab, pc[0], det24x);
   xlen = scale_expansion_zeroelim(xlen, det24x, pc[0], det48x);
   ylen = scale_expansion_zeroelim(dablen, dab, pc[1], det24y);
   ylen = scale_expansion_zeroelim(ylen, det24y, pc[1], det48y);
   clen = fast_expansion_sum_zeroelim(xlen, det48x, ylen, det48y, cdet);

   xlen = scale_expansion_zeroelim(abclen, abc, pd[0], det24x);
   xlen = scale_expansion_zeroelim(xlen, det24x, -pd[0], det48x);
   ylen = scale_expansion_zeroelim(abclen, abc, pd[1], det24y);
   ylen = scale_expansion_zeroelim(ylen, det24y, -pd[1], det48y);
   dlen = fast_expansion_sum_zeroelim(xlen, det48x, ylen, det48y, ddet);

   ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
   cdlen = fast_expansion_sum_zeroelim(clen, cdet, dlen, ddet, cddet);
   deterlen = fast_expansion_sum_zeroelim(ablen, abdet, cdlen, cddet, deter);

   return deter[deterlen - 1];
}

REAL incircleslow(REAL *pa, REAL *pb, REAL *pc, REAL *pd)
{
   INEXACT REAL adx, bdx, cdx, ady, bdy, cdy;
   REAL adxtail, bdxtail, cdxtail;
   REAL adytail, bdytail, cdytail;
   REAL negate, negatetail;
   INEXACT REAL axby7, bxcy7, axcy7, bxay7, cxby7, cxay7;
   REAL axby[8], bxcy[8], axcy[8], bxay[8], cxby[8], cxay[8];
   REAL temp16[16];
   int temp16len;
   REAL detx[32], detxx[64], detxt[32], detxxt[64], detxtxt[64];
   int xlen, xxlen, xtlen, xxtlen, xtxtlen;
   REAL x1[128], x2[192];
   int x1len, x2len;
   REAL dety[32], detyy[64], detyt[32], detyyt[64], detytyt[64];
   int ylen, yylen, ytlen, yytlen, ytytlen;
   REAL y1[128], y2[192];
   int y1len, y2len;
   REAL adet[384], bdet[384], cdet[384], abdet[768], deter[1152];
   int alen, blen, clen, ablen, deterlen;
   int i;

   INEXACT REAL bvirt;
   REAL avirt, bround, around;
   INEXACT REAL c;
   INEXACT REAL abig;
   REAL a0hi, a0lo, a1hi, a1lo, bhi, blo;
   REAL err1, err2, err3;
   INEXACT REAL _i, _j, _k, _l, _m, _n;
   REAL _0, _1, _2;

   Two_Diff(pa[0], pd[0], adx, adxtail);
   Two_Diff(pa[1], pd[1], ady, adytail);
   Two_Diff(pb[0], pd[0], bdx, bdxtail);
   Two_Diff(pb[1], pd[1], bdy, bdytail);
   Two_Diff(pc[0], pd[0], cdx, cdxtail);
   Two_Diff(pc[1], pd[1], cdy, cdytail);

   Two_Two_Product(adx, adxtail, bdy, bdytail,
      axby7, axby[6], axby[5], axby[4],
      axby[3], axby[2], axby[1], axby[0]);
   axby[7] = axby7;
   negate = -ady;
   negatetail = -adytail;
   Two_Two_Product(bdx, bdxtail, negate, negatetail,
      bxay7, bxay[6], bxay[5], bxay[4],
      bxay[3], bxay[2], bxay[1], bxay[0]);
   bxay[7] = bxay7;
   Two_Two_Product(bdx, bdxtail, cdy, cdytail,
      bxcy7, bxcy[6], bxcy[5], bxcy[4],
      bxcy[3], bxcy[2], bxcy[1], bxcy[0]);
   bxcy[7] = bxcy7;
   negate = -bdy;
   negatetail = -bdytail;
   Two_Two_Product(cdx, cdxtail, negate, negatetail,
      cxby7, cxby[6], cxby[5], cxby[4],
      cxby[3], cxby[2], cxby[1], cxby[0]);
   cxby[7] = cxby7;
   Two_Two_Product(cdx, cdxtail, ady, adytail,
      cxay7, cxay[6], cxay[5], cxay[4],
      cxay[3], cxay[2], cxay[1], cxay[0]);
   cxay[7] = cxay7;
   negate = -cdy;
   negatetail = -cdytail;
   Two_Two_Product(adx, adxtail, negate, negatetail,
      axcy7, axcy[6], axcy[5], axcy[4],
      axcy[3], axcy[2], axcy[1], axcy[0]);
   axcy[7] = axcy7;


   temp16len = fast_expansion_sum_zeroelim(8, bxcy, 8, cxby, temp16);

   xlen = scale_expansion_zeroelim(temp16len, temp16, adx, detx);
   xxlen = scale_expansion_zeroelim(xlen, detx, adx, detxx);
   xtlen = scale_expansion_zeroelim(temp16len, temp16, adxtail, detxt);
   xxtlen = scale_expansion_zeroelim(xtlen, detxt, adx, detxxt);
   for (i = 0; i < xxtlen; i++) {
      detxxt[i] *= 2.0;
   }
   xtxtlen = scale_expansion_zeroelim(xtlen, detxt, adxtail, detxtxt);
   x1len = fast_expansion_sum_zeroelim(xxlen, detxx, xxtlen, detxxt, x1);
   x2len = fast_expansion_sum_zeroelim(x1len, x1, xtxtlen, detxtxt, x2);

   ylen = scale_expansion_zeroelim(temp16len, temp16, ady, dety);
   yylen = scale_expansion_zeroelim(ylen, dety, ady, detyy);
   ytlen = scale_expansion_zeroelim(temp16len, temp16, adytail, detyt);
   yytlen = scale_expansion_zeroelim(ytlen, detyt, ady, detyyt);
   for (i = 0; i < yytlen; i++) {
      detyyt[i] *= 2.0;
   }
   ytytlen = scale_expansion_zeroelim(ytlen, detyt, adytail, detytyt);
   y1len = fast_expansion_sum_zeroelim(yylen, detyy, yytlen, detyyt, y1);
   y2len = fast_expansion_sum_zeroelim(y1len, y1, ytytlen, detytyt, y2);

   alen = fast_expansion_sum_zeroelim(x2len, x2, y2len, y2, adet);


   temp16len = fast_expansion_sum_zeroelim(8, cxay, 8, axcy, temp16);

   xlen = scale_expansion_zeroelim(temp16len, temp16, bdx, detx);
   xxlen = scale_expansion_zeroelim(xlen, detx, bdx, detxx);
   xtlen = scale_expansion_zeroelim(temp16len, temp16, bdxtail, detxt);
   xxtlen = scale_expansion_zeroelim(xtlen, detxt, bdx, detxxt);
   for (i = 0; i < xxtlen; i++) {
      detxxt[i] *= 2.0;
   }
   xtxtlen = scale_expansion_zeroelim(xtlen, detxt, bdxtail, detxtxt);
   x1len = fast_expansion_sum_zeroelim(xxlen, detxx, xxtlen, detxxt, x1);
   x2len = fast_expansion_sum_zeroelim(x1len, x1, xtxtlen, detxtxt, x2);

   ylen = scale_expansion_zeroelim(temp16len, temp16, bdy, dety);
   yylen = scale_expansion_zeroelim(ylen, dety, bdy, detyy);
   ytlen = scale_expansion_zeroelim(temp16len, temp16, bdytail, detyt);
   yytlen = scale_expansion_zeroelim(ytlen, detyt, bdy, detyyt);
   for (i = 0; i < yytlen; i++) {
      detyyt[i] *= 2.0;
   }
   ytytlen = scale_expansion_zeroelim(ytlen, detyt, bdytail, detytyt);
   y1len = fast_expansion_sum_zeroelim(yylen, detyy, yytlen, detyyt, y1);
   y2len = fast_expansion_sum_zeroelim(y1len, y1, ytytlen, detytyt, y2);

   blen = fast_expansion_sum_zeroelim(x2len, x2, y2len, y2, bdet);


   temp16len = fast_expansion_sum_zeroelim(8, axby, 8, bxay, temp16);

   xlen = scale_expansion_zeroelim(temp16len, temp16, cdx, detx);
   xxlen = scale_expansion_zeroelim(xlen, detx, cdx, detxx);
   xtlen = scale_expansion_zeroelim(temp16len, temp16, cdxtail, detxt);
   xxtlen = scale_expansion_zeroelim(xtlen, detxt, cdx, detxxt);
   for (i = 0; i < xxtlen; i++) {
      detxxt[i] *= 2.0;
   }
   xtxtlen = scale_expansion_zeroelim(xtlen, detxt, cdxtail, detxtxt);
   x1len = fast_expansion_sum_zeroelim(xxlen, detxx, xxtlen, detxxt, x1);
   x2len = fast_expansion_sum_zeroelim(x1len, x1, xtxtlen, detxtxt, x2);

   ylen = scale_expansion_zeroelim(temp16len, temp16, cdy, dety);
   yylen = scale_expansion_zeroelim(ylen, dety, cdy, detyy);
   ytlen = scale_expansion_zeroelim(temp16len, temp16, cdytail, detyt);
   yytlen = scale_expansion_zeroelim(ytlen, detyt, cdy, detyyt);
   for (i = 0; i < yytlen; i++) {
      detyyt[i] *= 2.0;
   }
   ytytlen = scale_expansion_zeroelim(ytlen, detyt, cdytail, detytyt);
   y1len = fast_expansion_sum_zeroelim(yylen, detyy, yytlen, detyyt, y1);
   y2len = fast_expansion_sum_zeroelim(y1len, y1, ytytlen, detytyt, y2);

   clen = fast_expansion_sum_zeroelim(x2len, x2, y2len, y2, cdet);

   ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
   deterlen = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, deter);

   return deter[deterlen - 1];
}

REAL incircleadapt(REAL *pa, REAL *pb, REAL *pc, REAL *pd, REAL permanent)
{
   INEXACT REAL adx, bdx, cdx, ady, bdy, cdy;
   REAL det, errbound;

   INEXACT REAL bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1;
   REAL bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0;
   REAL bc[4], ca[4], ab[4];
   INEXACT REAL bc3, ca3, ab3;
   REAL axbc[8], axxbc[16], aybc[8], ayybc[16], adet[32];
   int axbclen, axxbclen, aybclen, ayybclen, alen;
   REAL bxca[8], bxxca[16], byca[8], byyca[16], bdet[32];
   int bxcalen, bxxcalen, bycalen, byycalen, blen;
   REAL cxab[8], cxxab[16], cyab[8], cyyab[16], cdet[32];
   int cxablen, cxxablen, cyablen, cyyablen, clen;
   REAL abdet[64];
   int ablen;
   REAL fin1[1152], fin2[1152];
   REAL *finnow, *finother, *finswap;
   int finlength;

   REAL adxtail, bdxtail, cdxtail, adytail, bdytail, cdytail;
   INEXACT REAL adxadx1, adyady1, bdxbdx1, bdybdy1, cdxcdx1, cdycdy1;
   REAL adxadx0, adyady0, bdxbdx0, bdybdy0, cdxcdx0, cdycdy0;
   REAL aa[4], bb[4], cc[4];
   INEXACT REAL aa3, bb3, cc3;
   INEXACT REAL ti1, tj1;
   REAL ti0, tj0;
   REAL u[4], v[4];
   INEXACT REAL u3, v3;
   REAL temp8[8], temp16a[16], temp16b[16], temp16c[16];
   REAL temp32a[32], temp32b[32], temp48[48], temp64[64];
   int temp8len, temp16alen, temp16blen, temp16clen;
   int temp32alen, temp32blen, temp48len, temp64len;
   REAL axtbb[8], axtcc[8], aytbb[8], aytcc[8];
   int axtbblen, axtcclen, aytbblen, aytcclen;
   REAL bxtaa[8], bxtcc[8], bytaa[8], bytcc[8];
   int bxtaalen, bxtcclen, bytaalen, bytcclen;
   REAL cxtaa[8], cxtbb[8], cytaa[8], cytbb[8];
   int cxtaalen, cxtbblen, cytaalen, cytbblen;
   REAL axtbc[8], aytbc[8], bxtca[8], bytca[8], cxtab[8], cytab[8];
   int axtbclen, aytbclen, bxtcalen, bytcalen, cxtablen, cytablen;
   REAL axtbct[16], aytbct[16], bxtcat[16], bytcat[16], cxtabt[16], cytabt[16];
   int axtbctlen, aytbctlen, bxtcatlen, bytcatlen, cxtabtlen, cytabtlen;
   REAL axtbctt[8], aytbctt[8], bxtcatt[8];
   REAL bytcatt[8], cxtabtt[8], cytabtt[8];
   int axtbcttlen, aytbcttlen, bxtcattlen, bytcattlen, cxtabttlen, cytabttlen;
   REAL abt[8], bct[8], cat[8];
   int abtlen, bctlen, catlen;
   REAL abtt[4], bctt[4], catt[4];
   int abttlen, bcttlen, cattlen;
   INEXACT REAL abtt3, bctt3, catt3;
   REAL negate;

   INEXACT REAL bvirt;
   REAL avirt, bround, around;
   INEXACT REAL c;
   INEXACT REAL abig;
   REAL ahi, alo, bhi, blo;
   REAL err1, err2, err3;
   INEXACT REAL _i, _j;
   REAL _0;

   adx = (REAL) (pa[0] - pd[0]);
   bdx = (REAL) (pb[0] - pd[0]);
   cdx = (REAL) (pc[0] - pd[0]);
   ady = (REAL) (pa[1] - pd[1]);
   bdy = (REAL) (pb[1] - pd[1]);
   cdy = (REAL) (pc[1] - pd[1]);

   Two_Product(bdx, cdy, bdxcdy1, bdxcdy0);
   Two_Product(cdx, bdy, cdxbdy1, cdxbdy0);
   Two_Two_Diff(bdxcdy1, bdxcdy0, cdxbdy1, cdxbdy0, bc3, bc[2], bc[1], bc[0]);
   bc[3] = bc3;
   axbclen = scale_expansion_zeroelim(4, bc, adx, axbc);
   axxbclen = scale_expansion_zeroelim(axbclen, axbc, adx, axxbc);
   aybclen = scale_expansion_zeroelim(4, bc, ady, aybc);
   ayybclen = scale_expansion_zeroelim(aybclen, aybc, ady, ayybc);
   alen = fast_expansion_sum_zeroelim(axxbclen, axxbc, ayybclen, ayybc, adet);

   Two_Product(cdx, ady, cdxady1, cdxady0);
   Two_Product(adx, cdy, adxcdy1, adxcdy0);
   Two_Two_Diff(cdxady1, cdxady0, adxcdy1, adxcdy0, ca3, ca[2], ca[1], ca[0]);
   ca[3] = ca3;
   bxcalen = scale_expansion_zeroelim(4, ca, bdx, bxca);
   bxxcalen = scale_expansion_zeroelim(bxcalen, bxca, bdx, bxxca);
   bycalen = scale_expansion_zeroelim(4, ca, bdy, byca);
   byycalen = scale_expansion_zeroelim(bycalen, byca, bdy, byyca);
   blen = fast_expansion_sum_zeroelim(bxxcalen, bxxca, byycalen, byyca, bdet);

   Two_Product(adx, bdy, adxbdy1, adxbdy0);
   Two_Product(bdx, ady, bdxady1, bdxady0);
   Two_Two_Diff(adxbdy1, adxbdy0, bdxady1, bdxady0, ab3, ab[2], ab[1], ab[0]);
   ab[3] = ab3;
   cxablen = scale_expansion_zeroelim(4, ab, cdx, cxab);
   cxxablen = scale_expansion_zeroelim(cxablen, cxab, cdx, cxxab);
   cyablen = scale_expansion_zeroelim(4, ab, cdy, cyab);
   cyyablen = scale_expansion_zeroelim(cyablen, cyab, cdy, cyyab);
   clen = fast_expansion_sum_zeroelim(cxxablen, cxxab, cyyablen, cyyab, cdet);

   ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
   finlength = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, fin1);

   det = estimate(finlength, fin1);
   errbound = iccerrboundB * permanent;
   if ((det >= errbound) || (-det >= errbound)) {
      return det;
   }

   Two_Diff_Tail(pa[0], pd[0], adx, adxtail);
   Two_Diff_Tail(pa[1], pd[1], ady, adytail);
   Two_Diff_Tail(pb[0], pd[0], bdx, bdxtail);
   Two_Diff_Tail(pb[1], pd[1], bdy, bdytail);
   Two_Diff_Tail(pc[0], pd[0], cdx, cdxtail);
   Two_Diff_Tail(pc[1], pd[1], cdy, cdytail);
   if ((adxtail == 0.0) && (bdxtail == 0.0) && (cdxtail == 0.0)
      && (adytail == 0.0) && (bdytail == 0.0) && (cdytail == 0.0)) {
         return det;
   }

   errbound = iccerrboundC * permanent + resulterrbound * Absolute(det);
   det += ((adx * adx + ady * ady) * ((bdx * cdytail + cdy * bdxtail)
      - (bdy * cdxtail + cdx * bdytail))
      + 2.0 * (adx * adxtail + ady * adytail) * (bdx * cdy - bdy * cdx))
      + ((bdx * bdx + bdy * bdy) * ((cdx * adytail + ady * cdxtail)
      - (cdy * adxtail + adx * cdytail))
      + 2.0 * (bdx * bdxtail + bdy * bdytail) * (cdx * ady - cdy * adx))
      + ((cdx * cdx + cdy * cdy) * ((adx * bdytail + bdy * adxtail)
      - (ady * bdxtail + bdx * adytail))
      + 2.0 * (cdx * cdxtail + cdy * cdytail) * (adx * bdy - ady * bdx));
   if ((det >= errbound) || (-det >= errbound)) {
      return det;
   }

   finnow = fin1;
   finother = fin2;

   if ((bdxtail != 0.0) || (bdytail != 0.0)
      || (cdxtail != 0.0) || (cdytail != 0.0)) {
         Square(adx, adxadx1, adxadx0);
         Square(ady, adyady1, adyady0);
         Two_Two_Sum(adxadx1, adxadx0, adyady1, adyady0, aa3, aa[2], aa[1], aa[0]);
         aa[3] = aa3;
   }
   if ((cdxtail != 0.0) || (cdytail != 0.0)
      || (adxtail != 0.0) || (adytail != 0.0)) {
         Square(bdx, bdxbdx1, bdxbdx0);
         Square(bdy, bdybdy1, bdybdy0);
         Two_Two_Sum(bdxbdx1, bdxbdx0, bdybdy1, bdybdy0, bb3, bb[2], bb[1], bb[0]);
         bb[3] = bb3;
   }
   if ((adxtail != 0.0) || (adytail != 0.0)
      || (bdxtail != 0.0) || (bdytail != 0.0)) {
         Square(cdx, cdxcdx1, cdxcdx0);
         Square(cdy, cdycdy1, cdycdy0);
         Two_Two_Sum(cdxcdx1, cdxcdx0, cdycdy1, cdycdy0, cc3, cc[2], cc[1], cc[0]);
         cc[3] = cc3;
   }

   if (adxtail != 0.0) {
      axtbclen = scale_expansion_zeroelim(4, bc, adxtail, axtbc);
      temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, 2.0 * adx,
         temp16a);

      axtcclen = scale_expansion_zeroelim(4, cc, adxtail, axtcc);
      temp16blen = scale_expansion_zeroelim(axtcclen, axtcc, bdy, temp16b);

      axtbblen = scale_expansion_zeroelim(4, bb, adxtail, axtbb);
      temp16clen = scale_expansion_zeroelim(axtbblen, axtbb, -cdy, temp16c);

      temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
         temp16blen, temp16b, temp32a);
      temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
         temp32alen, temp32a, temp48);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
         temp48, finother);
      finswap = finnow; finnow = finother; finother = finswap;
   }
   if (adytail != 0.0) {
      aytbclen = scale_expansion_zeroelim(4, bc, adytail, aytbc);
      temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, 2.0 * ady,
         temp16a);

      aytbblen = scale_expansion_zeroelim(4, bb, adytail, aytbb);
      temp16blen = scale_expansion_zeroelim(aytbblen, aytbb, cdx, temp16b);

      aytcclen = scale_expansion_zeroelim(4, cc, adytail, aytcc);
      temp16clen = scale_expansion_zeroelim(aytcclen, aytcc, -bdx, temp16c);

      temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
         temp16blen, temp16b, temp32a);
      temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
         temp32alen, temp32a, temp48);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
         temp48, finother);
      finswap = finnow; finnow = finother; finother = finswap;
   }
   if (bdxtail != 0.0) {
      bxtcalen = scale_expansion_zeroelim(4, ca, bdxtail, bxtca);
      temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, 2.0 * bdx,
         temp16a);

      bxtaalen = scale_expansion_zeroelim(4, aa, bdxtail, bxtaa);
      temp16blen = scale_expansion_zeroelim(bxtaalen, bxtaa, cdy, temp16b);

      bxtcclen = scale_expansion_zeroelim(4, cc, bdxtail, bxtcc);
      temp16clen = scale_expansion_zeroelim(bxtcclen, bxtcc, -ady, temp16c);

      temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
         temp16blen, temp16b, temp32a);
      temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
         temp32alen, temp32a, temp48);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
         temp48, finother);
      finswap = finnow; finnow = finother; finother = finswap;
   }
   if (bdytail != 0.0) {
      bytcalen = scale_expansion_zeroelim(4, ca, bdytail, bytca);
      temp16alen = scale_expansion_zeroelim(bytcalen, bytca, 2.0 * bdy,
         temp16a);

      bytcclen = scale_expansion_zeroelim(4, cc, bdytail, bytcc);
      temp16blen = scale_expansion_zeroelim(bytcclen, bytcc, adx, temp16b);

      bytaalen = scale_expansion_zeroelim(4, aa, bdytail, bytaa);
      temp16clen = scale_expansion_zeroelim(bytaalen, bytaa, -cdx, temp16c);

      temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
         temp16blen, temp16b, temp32a);
      temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
         temp32alen, temp32a, temp48);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
         temp48, finother);
      finswap = finnow; finnow = finother; finother = finswap;
   }
   if (cdxtail != 0.0) {
      cxtablen = scale_expansion_zeroelim(4, ab, cdxtail, cxtab);
      temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, 2.0 * cdx,
         temp16a);

      cxtbblen = scale_expansion_zeroelim(4, bb, cdxtail, cxtbb);
      temp16blen = scale_expansion_zeroelim(cxtbblen, cxtbb, ady, temp16b);

      cxtaalen = scale_expansion_zeroelim(4, aa, cdxtail, cxtaa);
      temp16clen = scale_expansion_zeroelim(cxtaalen, cxtaa, -bdy, temp16c);

      temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
         temp16blen, temp16b, temp32a);
      temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
         temp32alen, temp32a, temp48);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
         temp48, finother);
      finswap = finnow; finnow = finother; finother = finswap;
   }
   if (cdytail != 0.0) {
      cytablen = scale_expansion_zeroelim(4, ab, cdytail, cytab);
      temp16alen = scale_expansion_zeroelim(cytablen, cytab, 2.0 * cdy,
         temp16a);

      cytaalen = scale_expansion_zeroelim(4, aa, cdytail, cytaa);
      temp16blen = scale_expansion_zeroelim(cytaalen, cytaa, bdx, temp16b);

      cytbblen = scale_expansion_zeroelim(4, bb, cdytail, cytbb);
      temp16clen = scale_expansion_zeroelim(cytbblen, cytbb, -adx, temp16c);

      temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
         temp16blen, temp16b, temp32a);
      temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
         temp32alen, temp32a, temp48);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
         temp48, finother);
      finswap = finnow; finnow = finother; finother = finswap;
   }

   if ((adxtail != 0.0) || (adytail != 0.0)) {
      if ((bdxtail != 0.0) || (bdytail != 0.0)
         || (cdxtail != 0.0) || (cdytail != 0.0)) {
            Two_Product(bdxtail, cdy, ti1, ti0);
            Two_Product(bdx, cdytail, tj1, tj0);
            Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
            u[3] = u3;
            negate = -bdy;
            Two_Product(cdxtail, negate, ti1, ti0);
            negate = -bdytail;
            Two_Product(cdx, negate, tj1, tj0);
            Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
            v[3] = v3;
            bctlen = fast_expansion_sum_zeroelim(4, u, 4, v, bct);

            Two_Product(bdxtail, cdytail, ti1, ti0);
            Two_Product(cdxtail, bdytail, tj1, tj0);
            Two_Two_Diff(ti1, ti0, tj1, tj0, bctt3, bctt[2], bctt[1], bctt[0]);
            bctt[3] = bctt3;
            bcttlen = 4;
      } else {
         bct[0] = 0.0;
         bctlen = 1;
         bctt[0] = 0.0;
         bcttlen = 1;
      }

      if (adxtail != 0.0) {
         temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, adxtail, temp16a);
         axtbctlen = scale_expansion_zeroelim(bctlen, bct, adxtail, axtbct);
         temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, 2.0 * adx,
            temp32a);
         temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
            temp32alen, temp32a, temp48);
         finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
            temp48, finother);
         finswap = finnow; finnow = finother; finother = finswap;
         if (bdytail != 0.0) {
            temp8len = scale_expansion_zeroelim(4, cc, adxtail, temp8);
            temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail,
               temp16a);
            finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
               temp16a, finother);
            finswap = finnow; finnow = finother; finother = finswap;
         }
         if (cdytail != 0.0) {
            temp8len = scale_expansion_zeroelim(4, bb, -adxtail, temp8);
            temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail,
               temp16a);
            finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
               temp16a, finother);
            finswap = finnow; finnow = finother; finother = finswap;
         }

         temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, adxtail,
            temp32a);
         axtbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adxtail, axtbctt);
         temp16alen = scale_expansion_zeroelim(axtbcttlen, axtbctt, 2.0 * adx,
            temp16a);
         temp16blen = scale_expansion_zeroelim(axtbcttlen, axtbctt, adxtail,
            temp16b);
         temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
            temp16blen, temp16b, temp32b);
         temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
            temp32blen, temp32b, temp64);
         finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
            temp64, finother);
         finswap = finnow; finnow = finother; finother = finswap;
      }
      if (adytail != 0.0) {
         temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, adytail, temp16a);
         aytbctlen = scale_expansion_zeroelim(bctlen, bct, adytail, aytbct);
         temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, 2.0 * ady,
            temp32a);
         temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
            temp32alen, temp32a, temp48);
         finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
            temp48, finother);
         finswap = finnow; finnow = finother; finother = finswap;


         temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, adytail,
            temp32a);
         aytbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adytail, aytbctt);
         temp16alen = scale_expansion_zeroelim(aytbcttlen, aytbctt, 2.0 * ady,
            temp16a);
         temp16blen = scale_expansion_zeroelim(aytbcttlen, aytbctt, adytail,
            temp16b);
         temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
            temp16blen, temp16b, temp32b);
         temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
            temp32blen, temp32b, temp64);
         finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
            temp64, finother);
         finswap = finnow; finnow = finother; finother = finswap;
      }
   }
   if ((bdxtail != 0.0) || (bdytail != 0.0)) {
      if ((cdxtail != 0.0) || (cdytail != 0.0)
         || (adxtail != 0.0) || (adytail != 0.0)) {
            Two_Product(cdxtail, ady, ti1, ti0);
            Two_Product(cdx, adytail, tj1, tj0);
            Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
            u[3] = u3;
            negate = -cdy;
            Two_Product(adxtail, negate, ti1, ti0);
            negate = -cdytail;
            Two_Product(adx, negate, tj1, tj0);
            Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
            v[3] = v3;
            catlen = fast_expansion_sum_zeroelim(4, u, 4, v, cat);

            Two_Product(cdxtail, adytail, ti1, ti0);
            Two_Product(adxtail, cdytail, tj1, tj0);
            Two_Two_Diff(ti1, ti0, tj1, tj0, catt3, catt[2], catt[1], catt[0]);
            catt[3] = catt3;
            cattlen = 4;
      } else {
         cat[0] = 0.0;
         catlen = 1;
         catt[0] = 0.0;
         cattlen = 1;
      }

      if (bdxtail != 0.0) {
         temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, bdxtail, temp16a);
         bxtcatlen = scale_expansion_zeroelim(catlen, cat, bdxtail, bxtcat);
         temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, 2.0 * bdx,
            temp32a);
         temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
            temp32alen, temp32a, temp48);
         finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
            temp48, finother);
         finswap = finnow; finnow = finother; finother = finswap;
         if (cdytail != 0.0) {
            temp8len = scale_expansion_zeroelim(4, aa, bdxtail, temp8);
            temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail,
               temp16a);
            finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
               temp16a, finother);
            finswap = finnow; finnow = finother; finother = finswap;
         }
         if (adytail != 0.0) {
            temp8len = scale_expansion_zeroelim(4, cc, -bdxtail, temp8);
            temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail,
               temp16a);
            finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
               temp16a, finother);
            finswap = finnow; finnow = finother; finother = finswap;
         }

         temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, bdxtail,
            temp32a);
         bxtcattlen = scale_expansion_zeroelim(cattlen, catt, bdxtail, bxtcatt);
         temp16alen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, 2.0 * bdx,
            temp16a);
         temp16blen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, bdxtail,
            temp16b);
         temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
            temp16blen, temp16b, temp32b);
         temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
            temp32blen, temp32b, temp64);
         finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
            temp64, finother);
         finswap = finnow; finnow = finother; finother = finswap;
      }
      if (bdytail != 0.0) {
         temp16alen = scale_expansion_zeroelim(bytcalen, bytca, bdytail, temp16a);
         bytcatlen = scale_expansion_zeroelim(catlen, cat, bdytail, bytcat);
         temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, 2.0 * bdy,
            temp32a);
         temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
            temp32alen, temp32a, temp48);
         finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
            temp48, finother);
         finswap = finnow; finnow = finother; finother = finswap;


         temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, bdytail,
            temp32a);
         bytcattlen = scale_expansion_zeroelim(cattlen, catt, bdytail, bytcatt);
         temp16alen = scale_expansion_zeroelim(bytcattlen, bytcatt, 2.0 * bdy,
            temp16a);
         temp16blen = scale_expansion_zeroelim(bytcattlen, bytcatt, bdytail,
            temp16b);
         temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
            temp16blen, temp16b, temp32b);
         temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
            temp32blen, temp32b, temp64);
         finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
            temp64, finother);
         finswap = finnow; finnow = finother; finother = finswap;
      }
   }
   if ((cdxtail != 0.0) || (cdytail != 0.0)) {
      if ((adxtail != 0.0) || (adytail != 0.0)
         || (bdxtail != 0.0) || (bdytail != 0.0)) {
            Two_Product(adxtail, bdy, ti1, ti0);
            Two_Product(adx, bdytail, tj1, tj0);
            Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
            u[3] = u3;
            negate = -ady;
            Two_Product(bdxtail, negate, ti1, ti0);
            negate = -adytail;
            Two_Product(bdx, negate, tj1, tj0);
            Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
            v[3] = v3;
            abtlen = fast_expansion_sum_zeroelim(4, u, 4, v, abt);

            Two_Product(adxtail, bdytail, ti1, ti0);
            Two_Product(bdxtail, adytail, tj1, tj0);
            Two_Two_Diff(ti1, ti0, tj1, tj0, abtt3, abtt[2], abtt[1], abtt[0]);
            abtt[3] = abtt3;
            abttlen = 4;
      } else {
         abt[0] = 0.0;
         abtlen = 1;
         abtt[0] = 0.0;
         abttlen = 1;
      }

      if (cdxtail != 0.0) {
         temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, cdxtail, temp16a);
         cxtabtlen = scale_expansion_zeroelim(abtlen, abt, cdxtail, cxtabt);
         temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, 2.0 * cdx,
            temp32a);
         temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
            temp32alen, temp32a, temp48);
         finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
            temp48, finother);
         finswap = finnow; finnow = finother; finother = finswap;
         if (adytail != 0.0) {
            temp8len = scale_expansion_zeroelim(4, bb, cdxtail, temp8);
            temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail,
               temp16a);
            finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
               temp16a, finother);
            finswap = finnow; finnow = finother; finother = finswap;
         }
         if (bdytail != 0.0) {
            temp8len = scale_expansion_zeroelim(4, aa, -cdxtail, temp8);
            temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail,
               temp16a);
            finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
               temp16a, finother);
            finswap = finnow; finnow = finother; finother = finswap;
         }

         temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, cdxtail,
            temp32a);
         cxtabttlen = scale_expansion_zeroelim(abttlen, abtt, cdxtail, cxtabtt);
         temp16alen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, 2.0 * cdx,
            temp16a);
         temp16blen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, cdxtail,
            temp16b);
         temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
            temp16blen, temp16b, temp32b);
         temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
            temp32blen, temp32b, temp64);
         finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
            temp64, finother);
         finswap = finnow; finnow = finother; finother = finswap;
      }
      if (cdytail != 0.0) {
         temp16alen = scale_expansion_zeroelim(cytablen, cytab, cdytail, temp16a);
         cytabtlen = scale_expansion_zeroelim(abtlen, abt, cdytail, cytabt);
         temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, 2.0 * cdy,
            temp32a);
         temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
            temp32alen, temp32a, temp48);
         finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
            temp48, finother);
         finswap = finnow; finnow = finother; finother = finswap;


         temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, cdytail,
            temp32a);
         cytabttlen = scale_expansion_zeroelim(abttlen, abtt, cdytail, cytabtt);
         temp16alen = scale_expansion_zeroelim(cytabttlen, cytabtt, 2.0 * cdy,
            temp16a);
         temp16blen = scale_expansion_zeroelim(cytabttlen, cytabtt, cdytail,
            temp16b);
         temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
            temp16blen, temp16b, temp32b);
         temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
            temp32blen, temp32b, temp64);
         finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
            temp64, finother);
         finswap = finnow; finnow = finother; finother = finswap;
      }
   }

   return finnow[finlength - 1];
}

REAL incircle(REAL *pa, REAL *pb, REAL *pc, REAL *pd)
{
   REAL adx, bdx, cdx, ady, bdy, cdy;
   REAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady;
   REAL alift, blift, clift;
   REAL det;
   REAL permanent, errbound;

   adx = pa[0] - pd[0];
   bdx = pb[0] - pd[0];
   cdx = pc[0] - pd[0];
   ady = pa[1] - pd[1];
   bdy = pb[1] - pd[1];
   cdy = pc[1] - pd[1];

   bdxcdy = bdx * cdy;
   cdxbdy = cdx * bdy;
   alift = adx * adx + ady * ady;

   cdxady = cdx * ady;
   adxcdy = adx * cdy;
   blift = bdx * bdx + bdy * bdy;

   adxbdy = adx * bdy;
   bdxady = bdx * ady;
   clift = cdx * cdx + cdy * cdy;

   det = alift * (bdxcdy - cdxbdy)
      + blift * (cdxady - adxcdy)
      + clift * (adxbdy - bdxady);

   permanent = (Absolute(bdxcdy) + Absolute(cdxbdy)) * alift
      + (Absolute(cdxady) + Absolute(adxcdy)) * blift
      + (Absolute(adxbdy) + Absolute(bdxady)) * clift;
   errbound = iccerrboundA * permanent;
   if ((det > errbound) || (-det > errbound)) {
      return det;
   }

   return incircleadapt(pa, pb, pc, pd, permanent);
}

/*****************************************************************************/
/*                                                                           */
/*  inspherefast()   Approximate 3D insphere test.  Nonrobust.               */
/*  insphereexact()   Exact 3D insphere test.  Robust.                       */
/*  insphereslow()   Another exact 3D insphere test.  Robust.                */
/*  insphere()   Adaptive exact 3D insphere test.  Robust.                   */
/*                                                                           */
/*               Return a positive value if the point pe lies inside the     */
/*               sphere passing through pa, pb, pc, and pd; a negative value */
/*               if it lies outside; and zero if the five points are         */
/*               cospherical.  The points pa, pb, pc, and pd must be ordered */
/*               so that they have a positive orientation (as defined by     */
/*               orient3d()), or the sign of the result will be reversed.    */
/*                                                                           */
/*  Only the first and last routine should be used; the middle two are for   */
/*  timings.                                                                 */
/*                                                                           */
/*  The last three use exact arithmetic to ensure a correct answer.  The     */
/*  result returned is the determinant of a matrix.  In insphere() only,     */
/*  this determinant is computed adaptively, in the sense that exact         */
/*  arithmetic is used only to the degree it is needed to ensure that the    */
/*  returned value has the correct sign.  Hence, insphere() is usually quite */
/*  fast, but will run more slowly when the input points are cospherical or  */
/*  nearly so.                                                               */
/*                                                                           */
/*****************************************************************************/

REAL inspherefast(REAL *pa, REAL *pb, REAL *pc, REAL *pd, REAL *pe)
{
   REAL aex, bex, cex, dex;
   REAL aey, bey, cey, dey;
   REAL aez, bez, cez, dez;
   REAL alift, blift, clift, dlift;
   REAL ab, bc, cd, da, ac, bd;
   REAL abc, bcd, cda, dab;

   aex = pa[0] - pe[0];
   bex = pb[0] - pe[0];
   cex = pc[0] - pe[0];
   dex = pd[0] - pe[0];
   aey = pa[1] - pe[1];
   bey = pb[1] - pe[1];
   cey = pc[1] - pe[1];
   dey = pd[1] - pe[1];
   aez = pa[2] - pe[2];
   bez = pb[2] - pe[2];
   cez = pc[2] - pe[2];
   dez = pd[2] - pe[2];

   ab = aex * bey - bex * aey;
   bc = bex * cey - cex * bey;
   cd = cex * dey - dex * cey;
   da = dex * aey - aex * dey;

   ac = aex * cey - cex * aey;
   bd = bex * dey - dex * bey;

   abc = aez * bc - bez * ac + cez * ab;
   bcd = bez * cd - cez * bd + dez * bc;
   cda = cez * da + dez * ac + aez * cd;
   dab = dez * ab + aez * bd + bez * da;

   alift = aex * aex + aey * aey + aez * aez;
   blift = bex * bex + bey * bey + bez * bez;
   clift = cex * cex + cey * cey + cez * cez;
   dlift = dex * dex + dey * dey + dez * dez;

   return (dlift * abc - clift * dab) + (blift * cda - alift * bcd);
}

REAL insphereexact(REAL *pa, REAL *pb, REAL *pc, REAL *pd, REAL *pe)
{
   INEXACT REAL axby1, bxcy1, cxdy1, dxey1, exay1;
   INEXACT REAL bxay1, cxby1, dxcy1, exdy1, axey1;
   INEXACT REAL axcy1, bxdy1, cxey1, dxay1, exby1;
   INEXACT REAL cxay1, dxby1, excy1, axdy1, bxey1;
   REAL axby0, bxcy0, cxdy0, dxey0, exay0;
   REAL bxay0, cxby0, dxcy0, exdy0, axey0;
   REAL axcy0, bxdy0, cxey0, dxay0, exby0;
   REAL cxay0, dxby0, excy0, axdy0, bxey0;
   REAL ab[4], bc[4], cd[4], de[4], ea[4];
   REAL ac[4], bd[4], ce[4], da[4], eb[4];
   REAL temp8a[8], temp8b[8], temp16[16];
   int temp8alen, temp8blen, temp16len;
   REAL abc[24], bcd[24], cde[24], dea[24], eab[24];
   REAL abd[24], bce[24], cda[24], deb[24], eac[24];
   int abclen, bcdlen, cdelen, dealen, eablen;
   int abdlen, bcelen, cdalen, deblen, eaclen;
   REAL temp48a[48], temp48b[48];
   int temp48alen, temp48blen;
   REAL abcd[96], bcde[96], cdea[96], deab[96], eabc[96];
   int abcdlen, bcdelen, cdealen, deablen, eabclen;
   REAL temp192[192];
   REAL det384x[384], det384y[384], det384z[384];
   int xlen, ylen, zlen;
   REAL detxy[768];
   int xylen;
   REAL adet[1152], bdet[1152], cdet[1152], ddet[1152], edet[1152];
   int alen, blen, clen, dlen, elen;
   REAL abdet[2304], cddet[2304], cdedet[3456];
   int ablen, cdlen;
   REAL deter[5760];
   int deterlen;
   int i;

   INEXACT REAL bvirt;
   REAL avirt, bround, around;
   INEXACT REAL c;
   INEXACT REAL abig;
   REAL ahi, alo, bhi, blo;
   REAL err1, err2, err3;
   INEXACT REAL _i, _j;
   REAL _0;

   Two_Product(pa[0], pb[1], axby1, axby0);
   Two_Product(pb[0], pa[1], bxay1, bxay0);
   Two_Two_Diff(axby1, axby0, bxay1, bxay0, ab[3], ab[2], ab[1], ab[0]);

   Two_Product(pb[0], pc[1], bxcy1, bxcy0);
   Two_Product(pc[0], pb[1], cxby1, cxby0);
   Two_Two_Diff(bxcy1, bxcy0, cxby1, cxby0, bc[3], bc[2], bc[1], bc[0]);

   Two_Product(pc[0], pd[1], cxdy1, cxdy0);
   Two_Product(pd[0], pc[1], dxcy1, dxcy0);
   Two_Two_Diff(cxdy1, cxdy0, dxcy1, dxcy0, cd[3], cd[2], cd[1], cd[0]);

   Two_Product(pd[0], pe[1], dxey1, dxey0);
   Two_Product(pe[0], pd[1], exdy1, exdy0);
   Two_Two_Diff(dxey1, dxey0, exdy1, exdy0, de[3], de[2], de[1], de[0]);

   Two_Product(pe[0], pa[1], exay1, exay0);
   Two_Product(pa[0], pe[1], axey1, axey0);
   Two_Two_Diff(exay1, exay0, axey1, axey0, ea[3], ea[2], ea[1], ea[0]);

   Two_Product(pa[0], pc[1], axcy1, axcy0);
   Two_Product(pc[0], pa[1], cxay1, cxay0);
   Two_Two_Diff(axcy1, axcy0, cxay1, cxay0, ac[3], ac[2], ac[1], ac[0]);

   Two_Product(pb[0], pd[1], bxdy1, bxdy0);
   Two_Product(pd[0], pb[1], dxby1, dxby0);
   Two_Two_Diff(bxdy1, bxdy0, dxby1, dxby0, bd[3], bd[2], bd[1], bd[0]);

   Two_Product(pc[0], pe[1], cxey1, cxey0);
   Two_Product(pe[0], pc[1], excy1, excy0);
   Two_Two_Diff(cxey1, cxey0, excy1, excy0, ce[3], ce[2], ce[1], ce[0]);

   Two_Product(pd[0], pa[1], dxay1, dxay0);
   Two_Product(pa[0], pd[1], axdy1, axdy0);
   Two_Two_Diff(dxay1, dxay0, axdy1, axdy0, da[3], da[2], da[1], da[0]);

   Two_Product(pe[0], pb[1], exby1, exby0);
   Two_Product(pb[0], pe[1], bxey1, bxey0);
   Two_Two_Diff(exby1, exby0, bxey1, bxey0, eb[3], eb[2], eb[1], eb[0]);

   temp8alen = scale_expansion_zeroelim(4, bc, pa[2], temp8a);
   temp8blen = scale_expansion_zeroelim(4, ac, -pb[2], temp8b);
   temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp8blen, temp8b,
      temp16);
   temp8alen = scale_expansion_zeroelim(4, ab, pc[2], temp8a);
   abclen = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp16len, temp16,
      abc);

   temp8alen = scale_expansion_zeroelim(4, cd, pb[2], temp8a);
   temp8blen = scale_expansion_zeroelim(4, bd, -pc[2], temp8b);
   temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp8blen, temp8b,
      temp16);
   temp8alen = scale_expansion_zeroelim(4, bc, pd[2], temp8a);
   bcdlen = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp16len, temp16,
      bcd);

   temp8alen = scale_expansion_zeroelim(4, de, pc[2], temp8a);
   temp8blen = scale_expansion_zeroelim(4, ce, -pd[2], temp8b);
   temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp8blen, temp8b,
      temp16);
   temp8alen = scale_expansion_zeroelim(4, cd, pe[2], temp8a);
   cdelen = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp16len, temp16,
      cde);

   temp8alen = scale_expansion_zeroelim(4, ea, pd[2], temp8a);
   temp8blen = scale_expansion_zeroelim(4, da, -pe[2], temp8b);
   temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp8blen, temp8b,
      temp16);
   temp8alen = scale_expansion_zeroelim(4, de, pa[2], temp8a);
   dealen = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp16len, temp16,
      dea);

   temp8alen = scale_expansion_zeroelim(4, ab, pe[2], temp8a);
   temp8blen = scale_expansion_zeroelim(4, eb, -pa[2], temp8b);
   temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp8blen, temp8b,
      temp16);
   temp8alen = scale_expansion_zeroelim(4, ea, pb[2], temp8a);
   eablen = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp16len, temp16,
      eab);

   temp8alen = scale_expansion_zeroelim(4, bd, pa[2], temp8a);
   temp8blen = scale_expansion_zeroelim(4, da, pb[2], temp8b);
   temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp8blen, temp8b,
      temp16);
   temp8alen = scale_expansion_zeroelim(4, ab, pd[2], temp8a);
   abdlen = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp16len, temp16,
      abd);

   temp8alen = scale_expansion_zeroelim(4, ce, pb[2], temp8a);
   temp8blen = scale_expansion_zeroelim(4, eb, pc[2], temp8b);
   temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp8blen, temp8b,
      temp16);
   temp8alen = scale_expansion_zeroelim(4, bc, pe[2], temp8a);
   bcelen = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp16len, temp16,
      bce);

   temp8alen = scale_expansion_zeroelim(4, da, pc[2], temp8a);
   temp8blen = scale_expansion_zeroelim(4, ac, pd[2], temp8b);
   temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp8blen, temp8b,
      temp16);
   temp8alen = scale_expansion_zeroelim(4, cd, pa[2], temp8a);
   cdalen = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp16len, temp16,
      cda);

   temp8alen = scale_expansion_zeroelim(4, eb, pd[2], temp8a);
   temp8blen = scale_expansion_zeroelim(4, bd, pe[2], temp8b);
   temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp8blen, temp8b,
      temp16);
   temp8alen = scale_expansion_zeroelim(4, de, pb[2], temp8a);
   deblen = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp16len, temp16,
      deb);

   temp8alen = scale_expansion_zeroelim(4, ac, pe[2], temp8a);
   temp8blen = scale_expansion_zeroelim(4, ce, pa[2], temp8b);
   temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp8blen, temp8b,
      temp16);
   temp8alen = scale_expansion_zeroelim(4, ea, pc[2], temp8a);
   eaclen = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp16len, temp16,
      eac);

   temp48alen = fast_expansion_sum_zeroelim(cdelen, cde, bcelen, bce, temp48a);
   temp48blen = fast_expansion_sum_zeroelim(deblen, deb, bcdlen, bcd, temp48b);
   for (i = 0; i < temp48blen; i++) {
      temp48b[i] = -temp48b[i];
   }
   bcdelen = fast_expansion_sum_zeroelim(temp48alen, temp48a,
      temp48blen, temp48b, bcde);
   xlen = scale_expansion_zeroelim(bcdelen, bcde, pa[0], temp192);
   xlen = scale_expansion_zeroelim(xlen, temp192, pa[0], det384x);
   ylen = scale_expansion_zeroelim(bcdelen, bcde, pa[1], temp192);
   ylen = scale_expansion_zeroelim(ylen, temp192, pa[1], det384y);
   zlen = scale_expansion_zeroelim(bcdelen, bcde, pa[2], temp192);
   zlen = scale_expansion_zeroelim(zlen, temp192, pa[2], det384z);
   xylen = fast_expansion_sum_zeroelim(xlen, det384x, ylen, det384y, detxy);
   alen = fast_expansion_sum_zeroelim(xylen, detxy, zlen, det384z, adet);

   temp48alen = fast_expansion_sum_zeroelim(dealen, dea, cdalen, cda, temp48a);
   temp48blen = fast_expansion_sum_zeroelim(eaclen, eac, cdelen, cde, temp48b);
   for (i = 0; i < temp48blen; i++) {
      temp48b[i] = -temp48b[i];
   }
   cdealen = fast_expansion_sum_zeroelim(temp48alen, temp48a,
      temp48blen, temp48b, cdea);
   xlen = scale_expansion_zeroelim(cdealen, cdea, pb[0], temp192);
   xlen = scale_expansion_zeroelim(xlen, temp192, pb[0], det384x);
   ylen = scale_expansion_zeroelim(cdealen, cdea, pb[1], temp192);
   ylen = scale_expansion_zeroelim(ylen, temp192, pb[1], det384y);
   zlen = scale_expansion_zeroelim(cdealen, cdea, pb[2], temp192);
   zlen = scale_expansion_zeroelim(zlen, temp192, pb[2], det384z);
   xylen = fast_expansion_sum_zeroelim(xlen, det384x, ylen, det384y, detxy);
   blen = fast_expansion_sum_zeroelim(xylen, detxy, zlen, det384z, bdet);

   temp48alen = fast_expansion_sum_zeroelim(eablen, eab, deblen, deb, temp48a);
   temp48blen = fast_expansion_sum_zeroelim(abdlen, abd, dealen, dea, temp48b);
   for (i = 0; i < temp48blen; i++) {
      temp48b[i] = -temp48b[i];
   }
   deablen = fast_expansion_sum_zeroelim(temp48alen, temp48a,
      temp48blen, temp48b, deab);
   xlen = scale_expansion_zeroelim(deablen, deab, pc[0], temp192);
   xlen = scale_expansion_zeroelim(xlen, temp192, pc[0], det384x);
   ylen = scale_expansion_zeroelim(deablen, deab, pc[1], temp192);
   ylen = scale_expansion_zeroelim(ylen, temp192, pc[1], det384y);
   zlen = scale_expansion_zeroelim(deablen, deab, pc[2], temp192);
   zlen = scale_expansion_zeroelim(zlen, temp192, pc[2], det384z);
   xylen = fast_expansion_sum_zeroelim(xlen, det384x, ylen, det384y, detxy);
   clen = fast_expansion_sum_zeroelim(xylen, detxy, zlen, det384z, cdet);

   temp48alen = fast_expansion_sum_zeroelim(abclen, abc, eaclen, eac, temp48a);
   temp48blen = fast_expansion_sum_zeroelim(bcelen, bce, eablen, eab, temp48b);
   for (i = 0; i < temp48blen; i++) {
      temp48b[i] = -temp48b[i];
   }
   eabclen = fast_expansion_sum_zeroelim(temp48alen, temp48a,
      temp48blen, temp48b, eabc);
   xlen = scale_expansion_zeroelim(eabclen, eabc, pd[0], temp192);
   xlen = scale_expansion_zeroelim(xlen, temp192, pd[0], det384x);
   ylen = scale_expansion_zeroelim(eabclen, eabc, pd[1], temp192);
   ylen = scale_expansion_zeroelim(ylen, temp192, pd[1], det384y);
   zlen = scale_expansion_zeroelim(eabclen, eabc, pd[2], temp192);
   zlen = scale_expansion_zeroelim(zlen, temp192, pd[2], det384z);
   xylen = fast_expansion_sum_zeroelim(xlen, det384x, ylen, det384y, detxy);
   dlen = fast_expansion_sum_zeroelim(xylen, detxy, zlen, det384z, ddet);

   temp48alen = fast_expansion_sum_zeroelim(bcdlen, bcd, abdlen, abd, temp48a);
   temp48blen = fast_expansion_sum_zeroelim(cdalen, cda, abclen, abc, temp48b);
   for (i = 0; i < temp48blen; i++) {
      temp48b[i] = -temp48b[i];
   }
   abcdlen = fast_expansion_sum_zeroelim(temp48alen, temp48a,
      temp48blen, temp48b, abcd);
   xlen = scale_expansion_zeroelim(abcdlen, abcd, pe[0], temp192);
   xlen = scale_expansion_zeroelim(xlen, temp192, pe[0], det384x);
   ylen = scale_expansion_zeroelim(abcdlen, abcd, pe[1], temp192);
   ylen = scale_expansion_zeroelim(ylen, temp192, pe[1], det384y);
   zlen = scale_expansion_zeroelim(abcdlen, abcd, pe[2], temp192);
   zlen = scale_expansion_zeroelim(zlen, temp192, pe[2], det384z);
   xylen = fast_expansion_sum_zeroelim(xlen, det384x, ylen, det384y, detxy);
   elen = fast_expansion_sum_zeroelim(xylen, detxy, zlen, det384z, edet);

   ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
   cdlen = fast_expansion_sum_zeroelim(clen, cdet, dlen, ddet, cddet);
   cdelen = fast_expansion_sum_zeroelim(cdlen, cddet, elen, edet, cdedet);
   deterlen = fast_expansion_sum_zeroelim(ablen, abdet, cdelen, cdedet, deter);

   return deter[deterlen - 1];
}

REAL insphereslow(REAL *pa, REAL *pb, REAL *pc, REAL *pd, REAL *pe)
{
   INEXACT REAL aex, bex, cex, dex, aey, bey, cey, dey, aez, bez, cez, dez;
   REAL aextail, bextail, cextail, dextail;
   REAL aeytail, beytail, ceytail, deytail;
   REAL aeztail, beztail, ceztail, deztail;
   REAL negate, negatetail;
   INEXACT REAL axby7, bxcy7, cxdy7, dxay7, axcy7, bxdy7;
   INEXACT REAL bxay7, cxby7, dxcy7, axdy7, cxay7, dxby7;
   REAL axby[8], bxcy[8], cxdy[8], dxay[8], axcy[8], bxdy[8];
   REAL bxay[8], cxby[8], dxcy[8], axdy[8], cxay[8], dxby[8];
   REAL ab[16], bc[16], cd[16], da[16], ac[16], bd[16];
   int ablen, bclen, cdlen, dalen, aclen, bdlen;
   REAL temp32a[32], temp32b[32], temp64a[64], temp64b[64], temp64c[64];
   int temp32alen, temp32blen, temp64alen, temp64blen, temp64clen;
   REAL temp128[128], temp192[192];
   int temp128len, temp192len;
   REAL detx[384], detxx[768], detxt[384], detxxt[768], detxtxt[768];
   int xlen, xxlen, xtlen, xxtlen, xtxtlen;
   REAL x1[1536], x2[2304];
   int x1len, x2len;
   REAL dety[384], detyy[768], detyt[384], detyyt[768], detytyt[768];
   int ylen, yylen, ytlen, yytlen, ytytlen;
   REAL y1[1536], y2[2304];
   int y1len, y2len;
   REAL detz[384], detzz[768], detzt[384], detzzt[768], detztzt[768];
   int zlen, zzlen, ztlen, zztlen, ztztlen;
   REAL z1[1536], z2[2304];
   int z1len, z2len;
   REAL detxy[4608];
   int xylen;
   REAL adet[6912], bdet[6912], cdet[6912], ddet[6912];
   int alen, blen, clen, dlen;
   REAL abdet[13824], cddet[13824], deter[27648];
   int deterlen;
   int i;

   INEXACT REAL bvirt;
   REAL avirt, bround, around;
   INEXACT REAL c;
   INEXACT REAL abig;
   REAL a0hi, a0lo, a1hi, a1lo, bhi, blo;
   REAL err1, err2, err3;
   INEXACT REAL _i, _j, _k, _l, _m, _n;
   REAL _0, _1, _2;

   Two_Diff(pa[0], pe[0], aex, aextail);
   Two_Diff(pa[1], pe[1], aey, aeytail);
   Two_Diff(pa[2], pe[2], aez, aeztail);
   Two_Diff(pb[0], pe[0], bex, bextail);
   Two_Diff(pb[1], pe[1], bey, beytail);
   Two_Diff(pb[2], pe[2], bez, beztail);
   Two_Diff(pc[0], pe[0], cex, cextail);
   Two_Diff(pc[1], pe[1], cey, ceytail);
   Two_Diff(pc[2], pe[2], cez, ceztail);
   Two_Diff(pd[0], pe[0], dex, dextail);
   Two_Diff(pd[1], pe[1], dey, deytail);
   Two_Diff(pd[2], pe[2], dez, deztail);

   Two_Two_Product(aex, aextail, bey, beytail,
      axby7, axby[6], axby[5], axby[4],
      axby[3], axby[2], axby[1], axby[0]);
   axby[7] = axby7;
   negate = -aey;
   negatetail = -aeytail;
   Two_Two_Product(bex, bextail, negate, negatetail,
      bxay7, bxay[6], bxay[5], bxay[4],
      bxay[3], bxay[2], bxay[1], bxay[0]);
   bxay[7] = bxay7;
   ablen = fast_expansion_sum_zeroelim(8, axby, 8, bxay, ab);
   Two_Two_Product(bex, bextail, cey, ceytail,
      bxcy7, bxcy[6], bxcy[5], bxcy[4],
      bxcy[3], bxcy[2], bxcy[1], bxcy[0]);
   bxcy[7] = bxcy7;
   negate = -bey;
   negatetail = -beytail;
   Two_Two_Product(cex, cextail, negate, negatetail,
      cxby7, cxby[6], cxby[5], cxby[4],
      cxby[3], cxby[2], cxby[1], cxby[0]);
   cxby[7] = cxby7;
   bclen = fast_expansion_sum_zeroelim(8, bxcy, 8, cxby, bc);
   Two_Two_Product(cex, cextail, dey, deytail,
      cxdy7, cxdy[6], cxdy[5], cxdy[4],
      cxdy[3], cxdy[2], cxdy[1], cxdy[0]);
   cxdy[7] = cxdy7;
   negate = -cey;
   negatetail = -ceytail;
   Two_Two_Product(dex, dextail, negate, negatetail,
      dxcy7, dxcy[6], dxcy[5], dxcy[4],
      dxcy[3], dxcy[2], dxcy[1], dxcy[0]);
   dxcy[7] = dxcy7;
   cdlen = fast_expansion_sum_zeroelim(8, cxdy, 8, dxcy, cd);
   Two_Two_Product(dex, dextail, aey, aeytail,
      dxay7, dxay[6], dxay[5], dxay[4],
      dxay[3], dxay[2], dxay[1], dxay[0]);
   dxay[7] = dxay7;
   negate = -dey;
   negatetail = -deytail;
   Two_Two_Product(aex, aextail, negate, negatetail,
      axdy7, axdy[6], axdy[5], axdy[4],
      axdy[3], axdy[2], axdy[1], axdy[0]);
   axdy[7] = axdy7;
   dalen = fast_expansion_sum_zeroelim(8, dxay, 8, axdy, da);
   Two_Two_Product(aex, aextail, cey, ceytail,
      axcy7, axcy[6], axcy[5], axcy[4],
      axcy[3], axcy[2], axcy[1], axcy[0]);
   axcy[7] = axcy7;
   negate = -aey;
   negatetail = -aeytail;
   Two_Two_Product(cex, cextail, negate, negatetail,
      cxay7, cxay[6], cxay[5], cxay[4],
      cxay[3], cxay[2], cxay[1], cxay[0]);
   cxay[7] = cxay7;
   aclen = fast_expansion_sum_zeroelim(8, axcy, 8, cxay, ac);
   Two_Two_Product(bex, bextail, dey, deytail,
      bxdy7, bxdy[6], bxdy[5], bxdy[4],
      bxdy[3], bxdy[2], bxdy[1], bxdy[0]);
   bxdy[7] = bxdy7;
   negate = -bey;
   negatetail = -beytail;
   Two_Two_Product(dex, dextail, negate, negatetail,
      dxby7, dxby[6], dxby[5], dxby[4],
      dxby[3], dxby[2], dxby[1], dxby[0]);
   dxby[7] = dxby7;
   bdlen = fast_expansion_sum_zeroelim(8, bxdy, 8, dxby, bd);

   temp32alen = scale_expansion_zeroelim(cdlen, cd, -bez, temp32a);
   temp32blen = scale_expansion_zeroelim(cdlen, cd, -beztail, temp32b);
   temp64alen = fast_expansion_sum_zeroelim(temp32alen, temp32a,
      temp32blen, temp32b, temp64a);
   temp32alen = scale_expansion_zeroelim(bdlen, bd, cez, temp32a);
   temp32blen = scale_expansion_zeroelim(bdlen, bd, ceztail, temp32b);
   temp64blen = fast_expansion_sum_zeroelim(temp32alen, temp32a,
      temp32blen, temp32b, temp64b);
   temp32alen = scale_expansion_zeroelim(bclen, bc, -dez, temp32a);
   temp32blen = scale_expansion_zeroelim(bclen, bc, -deztail, temp32b);
   temp64clen = fast_expansion_sum_zeroelim(temp32alen, temp32a,
      temp32blen, temp32b, temp64c);
   temp128len = fast_expansion_sum_zeroelim(temp64alen, temp64a,
      temp64blen, temp64b, temp128);
   temp192len = fast_expansion_sum_zeroelim(temp64clen, temp64c,
      temp128len, temp128, temp192);
   xlen = scale_expansion_zeroelim(temp192len, temp192, aex, detx);
   xxlen = scale_expansion_zeroelim(xlen, detx, aex, detxx);
   xtlen = scale_expansion_zeroelim(temp192len, temp192, aextail, detxt);
   xxtlen = scale_expansion_zeroelim(xtlen, detxt, aex, detxxt);
   for (i = 0; i < xxtlen; i++) {
      detxxt[i] *= 2.0;
   }
   xtxtlen = scale_expansion_zeroelim(xtlen, detxt, aextail, detxtxt);
   x1len = fast_expansion_sum_zeroelim(xxlen, detxx, xxtlen, detxxt, x1);
   x2len = fast_expansion_sum_zeroelim(x1len, x1, xtxtlen, detxtxt, x2);
   ylen = scale_expansion_zeroelim(temp192len, temp192, aey, dety);
   yylen = scale_expansion_zeroelim(ylen, dety, aey, detyy);
   ytlen = scale_expansion_zeroelim(temp192len, temp192, aeytail, detyt);
   yytlen = scale_expansion_zeroelim(ytlen, detyt, aey, detyyt);
   for (i = 0; i < yytlen; i++) {
      detyyt[i] *= 2.0;
   }
   ytytlen = scale_expansion_zeroelim(ytlen, detyt, aeytail, detytyt);
   y1len = fast_expansion_sum_zeroelim(yylen, detyy, yytlen, detyyt, y1);
   y2len = fast_expansion_sum_zeroelim(y1len, y1, ytytlen, detytyt, y2);
   zlen = scale_expansion_zeroelim(temp192len, temp192, aez, detz);
   zzlen = scale_expansion_zeroelim(zlen, detz, aez, detzz);
   ztlen = scale_expansion_zeroelim(temp192len, temp192, aeztail, detzt);
   zztlen = scale_expansion_zeroelim(ztlen, detzt, aez, detzzt);
   for (i = 0; i < zztlen; i++) {
      detzzt[i] *= 2.0;
   }
   ztztlen = scale_expansion_zeroelim(ztlen, detzt, aeztail, detztzt);
   z1len = fast_expansion_sum_zeroelim(zzlen, detzz, zztlen, detzzt, z1);
   z2len = fast_expansion_sum_zeroelim(z1len, z1, ztztlen, detztzt, z2);
   xylen = fast_expansion_sum_zeroelim(x2len, x2, y2len, y2, detxy);
   alen = fast_expansion_sum_zeroelim(z2len, z2, xylen, detxy, adet);

   temp32alen = scale_expansion_zeroelim(dalen, da, cez, temp32a);
   temp32blen = scale_expansion_zeroelim(dalen, da, ceztail, temp32b);
   temp64alen = fast_expansion_sum_zeroelim(temp32alen, temp32a,
      temp32blen, temp32b, temp64a);
   temp32alen = scale_expansion_zeroelim(aclen, ac, dez, temp32a);
   temp32blen = scale_expansion_zeroelim(aclen, ac, deztail, temp32b);
   temp64blen = fast_expansion_sum_zeroelim(temp32alen, temp32a,
      temp32blen, temp32b, temp64b);
   temp32alen = scale_expansion_zeroelim(cdlen, cd, aez, temp32a);
   temp32blen = scale_expansion_zeroelim(cdlen, cd, aeztail, temp32b);
   temp64clen = fast_expansion_sum_zeroelim(temp32alen, temp32a,
      temp32blen, temp32b, temp64c);
   temp128len = fast_expansion_sum_zeroelim(temp64alen, temp64a,
      temp64blen, temp64b, temp128);
   temp192len = fast_expansion_sum_zeroelim(temp64clen, temp64c,
      temp128len, temp128, temp192);
   xlen = scale_expansion_zeroelim(temp192len, temp192, bex, detx);
   xxlen = scale_expansion_zeroelim(xlen, detx, bex, detxx);
   xtlen = scale_expansion_zeroelim(temp192len, temp192, bextail, detxt);
   xxtlen = scale_expansion_zeroelim(xtlen, detxt, bex, detxxt);
   for (i = 0; i < xxtlen; i++) {
      detxxt[i] *= 2.0;
   }
   xtxtlen = scale_expansion_zeroelim(xtlen, detxt, bextail, detxtxt);
   x1len = fast_expansion_sum_zeroelim(xxlen, detxx, xxtlen, detxxt, x1);
   x2len = fast_expansion_sum_zeroelim(x1len, x1, xtxtlen, detxtxt, x2);
   ylen = scale_expansion_zeroelim(temp192len, temp192, bey, dety);
   yylen = scale_expansion_zeroelim(ylen, dety, bey, detyy);
   ytlen = scale_expansion_zeroelim(temp192len, temp192, beytail, detyt);
   yytlen = scale_expansion_zeroelim(ytlen, detyt, bey, detyyt);
   for (i = 0; i < yytlen; i++) {
      detyyt[i] *= 2.0;
   }
   ytytlen = scale_expansion_zeroelim(ytlen, detyt, beytail, detytyt);
   y1len = fast_expansion_sum_zeroelim(yylen, detyy, yytlen, detyyt, y1);
   y2len = fast_expansion_sum_zeroelim(y1len, y1, ytytlen, detytyt, y2);
   zlen = scale_expansion_zeroelim(temp192len, temp192, bez, detz);
   zzlen = scale_expansion_zeroelim(zlen, detz, bez, detzz);
   ztlen = scale_expansion_zeroelim(temp192len, temp192, beztail, detzt);
   zztlen = scale_expansion_zeroelim(ztlen, detzt, bez, detzzt);
   for (i = 0; i < zztlen; i++) {
      detzzt[i] *= 2.0;
   }
   ztztlen = scale_expansion_zeroelim(ztlen, detzt, beztail, detztzt);
   z1len = fast_expansion_sum_zeroelim(zzlen, detzz, zztlen, detzzt, z1);
   z2len = fast_expansion_sum_zeroelim(z1len, z1, ztztlen, detztzt, z2);
   xylen = fast_expansion_sum_zeroelim(x2len, x2, y2len, y2, detxy);
   blen = fast_expansion_sum_zeroelim(z2len, z2, xylen, detxy, bdet);

   temp32alen = scale_expansion_zeroelim(ablen, ab, -dez, temp32a);
   temp32blen = scale_expansion_zeroelim(ablen, ab, -deztail, temp32b);
   temp64alen = fast_expansion_sum_zeroelim(temp32alen, temp32a,
      temp32blen, temp32b, temp64a);
   temp32alen = scale_expansion_zeroelim(bdlen, bd, -aez, temp32a);
   temp32blen = scale_expansion_zeroelim(bdlen, bd, -aeztail, temp32b);
   temp64blen = fast_expansion_sum_zeroelim(temp32alen, temp32a,
      temp32blen, temp32b, temp64b);
   temp32alen = scale_expansion_zeroelim(dalen, da, -bez, temp32a);
   temp32blen = scale_expansion_zeroelim(dalen, da, -beztail, temp32b);
   temp64clen = fast_expansion_sum_zeroelim(temp32alen, temp32a,
      temp32blen, temp32b, temp64c);
   temp128len = fast_expansion_sum_zeroelim(temp64alen, temp64a,
      temp64blen, temp64b, temp128);
   temp192len = fast_expansion_sum_zeroelim(temp64clen, temp64c,
      temp128len, temp128, temp192);
   xlen = scale_expansion_zeroelim(temp192len, temp192, cex, detx);
   xxlen = scale_expansion_zeroelim(xlen, detx, cex, detxx);
   xtlen = scale_expansion_zeroelim(temp192len, temp192, cextail, detxt);
   xxtlen = scale_expansion_zeroelim(xtlen, detxt, cex, detxxt);
   for (i = 0; i < xxtlen; i++) {
      detxxt[i] *= 2.0;
   }
   xtxtlen = scale_expansion_zeroelim(xtlen, detxt, cextail, detxtxt);
   x1len = fast_expansion_sum_zeroelim(xxlen, detxx, xxtlen, detxxt, x1);
   x2len = fast_expansion_sum_zeroelim(x1len, x1, xtxtlen, detxtxt, x2);
   ylen = scale_expansion_zeroelim(temp192len, temp192, cey, dety);
   yylen = scale_expansion_zeroelim(ylen, dety, cey, detyy);
   ytlen = scale_expansion_zeroelim(temp192len, temp192, ceytail, detyt);
   yytlen = scale_expansion_zeroelim(ytlen, detyt, cey, detyyt);
   for (i = 0; i < yytlen; i++) {
      detyyt[i] *= 2.0;
   }
   ytytlen = scale_expansion_zeroelim(ytlen, detyt, ceytail, detytyt);
   y1len = fast_expansion_sum_zeroelim(yylen, detyy, yytlen, detyyt, y1);
   y2len = fast_expansion_sum_zeroelim(y1len, y1, ytytlen, detytyt, y2);
   zlen = scale_expansion_zeroelim(temp192len, temp192, cez, detz);
   zzlen = scale_expansion_zeroelim(zlen, detz, cez, detzz);
   ztlen = scale_expansion_zeroelim(temp192len, temp192, ceztail, detzt);
   zztlen = scale_expansion_zeroelim(ztlen, detzt, cez, detzzt);
   for (i = 0; i < zztlen; i++) {
      detzzt[i] *= 2.0;
   }
   ztztlen = scale_expansion_zeroelim(ztlen, detzt, ceztail, detztzt);
   z1len = fast_expansion_sum_zeroelim(zzlen, detzz, zztlen, detzzt, z1);
   z2len = fast_expansion_sum_zeroelim(z1len, z1, ztztlen, detztzt, z2);
   xylen = fast_expansion_sum_zeroelim(x2len, x2, y2len, y2, detxy);
   clen = fast_expansion_sum_zeroelim(z2len, z2, xylen, detxy, cdet);

   temp32alen = scale_expansion_zeroelim(bclen, bc, aez, temp32a);
   temp32blen = scale_expansion_zeroelim(bclen, bc, aeztail, temp32b);
   temp64alen = fast_expansion_sum_zeroelim(temp32alen, temp32a,
      temp32blen, temp32b, temp64a);
   temp32alen = scale_expansion_zeroelim(aclen, ac, -bez, temp32a);
   temp32blen = scale_expansion_zeroelim(aclen, ac, -beztail, temp32b);
   temp64blen = fast_expansion_sum_zeroelim(temp32alen, temp32a,
      temp32blen, temp32b, temp64b);
   temp32alen = scale_expansion_zeroelim(ablen, ab, cez, temp32a);
   temp32blen = scale_expansion_zeroelim(ablen, ab, ceztail, temp32b);
   temp64clen = fast_expansion_sum_zeroelim(temp32alen, temp32a,
      temp32blen, temp32b, temp64c);
   temp128len = fast_expansion_sum_zeroelim(temp64alen, temp64a,
      temp64blen, temp64b, temp128);
   temp192len = fast_expansion_sum_zeroelim(temp64clen, temp64c,
      temp128len, temp128, temp192);
   xlen = scale_expansion_zeroelim(temp192len, temp192, dex, detx);
   xxlen = scale_expansion_zeroelim(xlen, detx, dex, detxx);
   xtlen = scale_expansion_zeroelim(temp192len, temp192, dextail, detxt);
   xxtlen = scale_expansion_zeroelim(xtlen, detxt, dex, detxxt);
   for (i = 0; i < xxtlen; i++) {
      detxxt[i] *= 2.0;
   }
   xtxtlen = scale_expansion_zeroelim(xtlen, detxt, dextail, detxtxt);
   x1len = fast_expansion_sum_zeroelim(xxlen, detxx, xxtlen, detxxt, x1);
   x2len = fast_expansion_sum_zeroelim(x1len, x1, xtxtlen, detxtxt, x2);
   ylen = scale_expansion_zeroelim(temp192len, temp192, dey, dety);
   yylen = scale_expansion_zeroelim(ylen, dety, dey, detyy);
   ytlen = scale_expansion_zeroelim(temp192len, temp192, deytail, detyt);
   yytlen = scale_expansion_zeroelim(ytlen, detyt, dey, detyyt);
   for (i = 0; i < yytlen; i++) {
      detyyt[i] *= 2.0;
   }
   ytytlen = scale_expansion_zeroelim(ytlen, detyt, deytail, detytyt);
   y1len = fast_expansion_sum_zeroelim(yylen, detyy, yytlen, detyyt, y1);
   y2len = fast_expansion_sum_zeroelim(y1len, y1, ytytlen, detytyt, y2);
   zlen = scale_expansion_zeroelim(temp192len, temp192, dez, detz);
   zzlen = scale_expansion_zeroelim(zlen, detz, dez, detzz);
   ztlen = scale_expansion_zeroelim(temp192len, temp192, deztail, detzt);
   zztlen = scale_expansion_zeroelim(ztlen, detzt, dez, detzzt);
   for (i = 0; i < zztlen; i++) {
      detzzt[i] *= 2.0;
   }
   ztztlen = scale_expansion_zeroelim(ztlen, detzt, deztail, detztzt);
   z1len = fast_expansion_sum_zeroelim(zzlen, detzz, zztlen, detzzt, z1);
   z2len = fast_expansion_sum_zeroelim(z1len, z1, ztztlen, detztzt, z2);
   xylen = fast_expansion_sum_zeroelim(x2len, x2, y2len, y2, detxy);
   dlen = fast_expansion_sum_zeroelim(z2len, z2, xylen, detxy, ddet);

   ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
   cdlen = fast_expansion_sum_zeroelim(clen, cdet, dlen, ddet, cddet);
   deterlen = fast_expansion_sum_zeroelim(ablen, abdet, cdlen, cddet, deter);

   return deter[deterlen - 1];
}

REAL insphereadapt(REAL *pa, REAL *pb, REAL *pc, REAL *pd, REAL *pe,
                   REAL permanent)
{
   INEXACT REAL aex, bex, cex, dex, aey, bey, cey, dey, aez, bez, cez, dez;
   REAL det, errbound;

   INEXACT REAL aexbey1, bexaey1, bexcey1, cexbey1;
   INEXACT REAL cexdey1, dexcey1, dexaey1, aexdey1;
   INEXACT REAL aexcey1, cexaey1, bexdey1, dexbey1;
   REAL aexbey0, bexaey0, bexcey0, cexbey0;
   REAL cexdey0, dexcey0, dexaey0, aexdey0;
   REAL aexcey0, cexaey0, bexdey0, dexbey0;
   REAL ab[4], bc[4], cd[4], da[4], ac[4], bd[4];
   INEXACT REAL ab3, bc3, cd3, da3, ac3, bd3;
   REAL abeps, bceps, cdeps, daeps, aceps, bdeps;
   REAL temp8a[8], temp8b[8], temp8c[8], temp16[16], temp24[24], temp48[48];
   int temp8alen, temp8blen, temp8clen, temp16len, temp24len, temp48len;
   REAL xdet[96], ydet[96], zdet[96], xydet[192];
   int xlen, ylen, zlen, xylen;
   REAL adet[288], bdet[288], cdet[288], ddet[288];
   int alen, blen, clen, dlen;
   REAL abdet[576], cddet[576];
   int ablen, cdlen;
   REAL fin1[1152];
   int finlength;

   REAL aextail, bextail, cextail, dextail;
   REAL aeytail, beytail, ceytail, deytail;
   REAL aeztail, beztail, ceztail, deztail;

   INEXACT REAL bvirt;
   REAL avirt, bround, around;
   INEXACT REAL c;
   INEXACT REAL abig;
   REAL ahi, alo, bhi, blo;
   REAL err1, err2, err3;
   INEXACT REAL _i, _j;
   REAL _0;

   aex = (REAL) (pa[0] - pe[0]);
   bex = (REAL) (pb[0] - pe[0]);
   cex = (REAL) (pc[0] - pe[0]);
   dex = (REAL) (pd[0] - pe[0]);
   aey = (REAL) (pa[1] - pe[1]);
   bey = (REAL) (pb[1] - pe[1]);
   cey = (REAL) (pc[1] - pe[1]);
   dey = (REAL) (pd[1] - pe[1]);
   aez = (REAL) (pa[2] - pe[2]);
   bez = (REAL) (pb[2] - pe[2]);
   cez = (REAL) (pc[2] - pe[2]);
   dez = (REAL) (pd[2] - pe[2]);

   Two_Product(aex, bey, aexbey1, aexbey0);
   Two_Product(bex, aey, bexaey1, bexaey0);
   Two_Two_Diff(aexbey1, aexbey0, bexaey1, bexaey0, ab3, ab[2], ab[1], ab[0]);
   ab[3] = ab3;

   Two_Product(bex, cey, bexcey1, bexcey0);
   Two_Product(cex, bey, cexbey1, cexbey0);
   Two_Two_Diff(bexcey1, bexcey0, cexbey1, cexbey0, bc3, bc[2], bc[1], bc[0]);
   bc[3] = bc3;

   Two_Product(cex, dey, cexdey1, cexdey0);
   Two_Product(dex, cey, dexcey1, dexcey0);
   Two_Two_Diff(cexdey1, cexdey0, dexcey1, dexcey0, cd3, cd[2], cd[1], cd[0]);
   cd[3] = cd3;

   Two_Product(dex, aey, dexaey1, dexaey0);
   Two_Product(aex, dey, aexdey1, aexdey0);
   Two_Two_Diff(dexaey1, dexaey0, aexdey1, aexdey0, da3, da[2], da[1], da[0]);
   da[3] = da3;

   Two_Product(aex, cey, aexcey1, aexcey0);
   Two_Product(cex, aey, cexaey1, cexaey0);
   Two_Two_Diff(aexcey1, aexcey0, cexaey1, cexaey0, ac3, ac[2], ac[1], ac[0]);
   ac[3] = ac3;

   Two_Product(bex, dey, bexdey1, bexdey0);
   Two_Product(dex, bey, dexbey1, dexbey0);
   Two_Two_Diff(bexdey1, bexdey0, dexbey1, dexbey0, bd3, bd[2], bd[1], bd[0]);
   bd[3] = bd3;

   temp8alen = scale_expansion_zeroelim(4, cd, bez, temp8a);
   temp8blen = scale_expansion_zeroelim(4, bd, -cez, temp8b);
   temp8clen = scale_expansion_zeroelim(4, bc, dez, temp8c);
   temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a,
      temp8blen, temp8b, temp16);
   temp24len = fast_expansion_sum_zeroelim(temp8clen, temp8c,
      temp16len, temp16, temp24);
   temp48len = scale_expansion_zeroelim(temp24len, temp24, aex, temp48);
   xlen = scale_expansion_zeroelim(temp48len, temp48, -aex, xdet);
   temp48len = scale_expansion_zeroelim(temp24len, temp24, aey, temp48);
   ylen = scale_expansion_zeroelim(temp48len, temp48, -aey, ydet);
   temp48len = scale_expansion_zeroelim(temp24len, temp24, aez, temp48);
   zlen = scale_expansion_zeroelim(temp48len, temp48, -aez, zdet);
   xylen = fast_expansion_sum_zeroelim(xlen, xdet, ylen, ydet, xydet);
   alen = fast_expansion_sum_zeroelim(xylen, xydet, zlen, zdet, adet);

   temp8alen = scale_expansion_zeroelim(4, da, cez, temp8a);
   temp8blen = scale_expansion_zeroelim(4, ac, dez, temp8b);
   temp8clen = scale_expansion_zeroelim(4, cd, aez, temp8c);
   temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a,
      temp8blen, temp8b, temp16);
   temp24len = fast_expansion_sum_zeroelim(temp8clen, temp8c,
      temp16len, temp16, temp24);
   temp48len = scale_expansion_zeroelim(temp24len, temp24, bex, temp48);
   xlen = scale_expansion_zeroelim(temp48len, temp48, bex, xdet);
   temp48len = scale_expansion_zeroelim(temp24len, temp24, bey, temp48);
   ylen = scale_expansion_zeroelim(temp48len, temp48, bey, ydet);
   temp48len = scale_expansion_zeroelim(temp24len, temp24, bez, temp48);
   zlen = scale_expansion_zeroelim(temp48len, temp48, bez, zdet);
   xylen = fast_expansion_sum_zeroelim(xlen, xdet, ylen, ydet, xydet);
   blen = fast_expansion_sum_zeroelim(xylen, xydet, zlen, zdet, bdet);

   temp8alen = scale_expansion_zeroelim(4, ab, dez, temp8a);
   temp8blen = scale_expansion_zeroelim(4, bd, aez, temp8b);
   temp8clen = scale_expansion_zeroelim(4, da, bez, temp8c);
   temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a,
      temp8blen, temp8b, temp16);
   temp24len = fast_expansion_sum_zeroelim(temp8clen, temp8c,
      temp16len, temp16, temp24);
   temp48len = scale_expansion_zeroelim(temp24len, temp24, cex, temp48);
   xlen = scale_expansion_zeroelim(temp48len, temp48, -cex, xdet);
   temp48len = scale_expansion_zeroelim(temp24len, temp24, cey, temp48);
   ylen = scale_expansion_zeroelim(temp48len, temp48, -cey, ydet);
   temp48len = scale_expansion_zeroelim(temp24len, temp24, cez, temp48);
   zlen = scale_expansion_zeroelim(temp48len, temp48, -cez, zdet);
   xylen = fast_expansion_sum_zeroelim(xlen, xdet, ylen, ydet, xydet);
   clen = fast_expansion_sum_zeroelim(xylen, xydet, zlen, zdet, cdet);

   temp8alen = scale_expansion_zeroelim(4, bc, aez, temp8a);
   temp8blen = scale_expansion_zeroelim(4, ac, -bez, temp8b);
   temp8clen = scale_expansion_zeroelim(4, ab, cez, temp8c);
   temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a,
      temp8blen, temp8b, temp16);
   temp24len = fast_expansion_sum_zeroelim(temp8clen, temp8c,
      temp16len, temp16, temp24);
   temp48len = scale_expansion_zeroelim(temp24len, temp24, dex, temp48);
   xlen = scale_expansion_zeroelim(temp48len, temp48, dex, xdet);
   temp48len = scale_expansion_zeroelim(temp24len, temp24, dey, temp48);
   ylen = scale_expansion_zeroelim(temp48len, temp48, dey, ydet);
   temp48len = scale_expansion_zeroelim(temp24len, temp24, dez, temp48);
   zlen = scale_expansion_zeroelim(temp48len, temp48, dez, zdet);
   xylen = fast_expansion_sum_zeroelim(xlen, xdet, ylen, ydet, xydet);
   dlen = fast_expansion_sum_zeroelim(xylen, xydet, zlen, zdet, ddet);

   ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
   cdlen = fast_expansion_sum_zeroelim(clen, cdet, dlen, ddet, cddet);
   finlength = fast_expansion_sum_zeroelim(ablen, abdet, cdlen, cddet, fin1);

   det = estimate(finlength, fin1);
   errbound = isperrboundB * permanent;
   if ((det >= errbound) || (-det >= errbound)) {
      return det;
   }

   Two_Diff_Tail(pa[0], pe[0], aex, aextail);
   Two_Diff_Tail(pa[1], pe[1], aey, aeytail);
   Two_Diff_Tail(pa[2], pe[2], aez, aeztail);
   Two_Diff_Tail(pb[0], pe[0], bex, bextail);
   Two_Diff_Tail(pb[1], pe[1], bey, beytail);
   Two_Diff_Tail(pb[2], pe[2], bez, beztail);
   Two_Diff_Tail(pc[0], pe[0], cex, cextail);
   Two_Diff_Tail(pc[1], pe[1], cey, ceytail);
   Two_Diff_Tail(pc[2], pe[2], cez, ceztail);
   Two_Diff_Tail(pd[0], pe[0], dex, dextail);
   Two_Diff_Tail(pd[1], pe[1], dey, deytail);
   Two_Diff_Tail(pd[2], pe[2], dez, deztail);
   if ((aextail == 0.0) && (aeytail == 0.0) && (aeztail == 0.0)
      && (bextail == 0.0) && (beytail == 0.0) && (beztail == 0.0)
      && (cextail == 0.0) && (ceytail == 0.0) && (ceztail == 0.0)
      && (dextail == 0.0) && (deytail == 0.0) && (deztail == 0.0)) {
         return det;
   }

   errbound = isperrboundC * permanent + resulterrbound * Absolute(det);
   abeps = (aex * beytail + bey * aextail)
      - (aey * bextail + bex * aeytail);
   bceps = (bex * ceytail + cey * bextail)
      - (bey * cextail + cex * beytail);
   cdeps = (cex * deytail + dey * cextail)
      - (cey * dextail + dex * ceytail);
   daeps = (dex * aeytail + aey * dextail)
      - (dey * aextail + aex * deytail);
   aceps = (aex * ceytail + cey * aextail)
      - (aey * cextail + cex * aeytail);
   bdeps = (bex * deytail + dey * bextail)
      - (bey * dextail + dex * beytail);
   det += (((bex * bex + bey * bey + bez * bez)
      * ((cez * daeps + dez * aceps + aez * cdeps)
      + (ceztail * da3 + deztail * ac3 + aeztail * cd3))
      + (dex * dex + dey * dey + dez * dez)
      * ((aez * bceps - bez * aceps + cez * abeps)
      + (aeztail * bc3 - beztail * ac3 + ceztail * ab3)))
      - ((aex * aex + aey * aey + aez * aez)
      * ((bez * cdeps - cez * bdeps + dez * bceps)
      + (beztail * cd3 - ceztail * bd3 + deztail * bc3))
      + (cex * cex + cey * cey + cez * cez)
      * ((dez * abeps + aez * bdeps + bez * daeps)
      + (deztail * ab3 + aeztail * bd3 + beztail * da3))))
      + 2.0 * (((bex * bextail + bey * beytail + bez * beztail)
      * (cez * da3 + dez * ac3 + aez * cd3)
      + (dex * dextail + dey * deytail + dez * deztail)
      * (aez * bc3 - bez * ac3 + cez * ab3))
      - ((aex * aextail + aey * aeytail + aez * aeztail)
      * (bez * cd3 - cez * bd3 + dez * bc3)
      + (cex * cextail + cey * ceytail + cez * ceztail)
      * (dez * ab3 + aez * bd3 + bez * da3)));
   if ((det >= errbound) || (-det >= errbound)) {
      return det;
   }

   return insphereexact(pa, pb, pc, pd, pe);
}

REAL insphere(REAL *pa, REAL *pb, REAL *pc, REAL *pd, REAL *pe)
{
   REAL aex, bex, cex, dex;
   REAL aey, bey, cey, dey;
   REAL aez, bez, cez, dez;
   REAL aexbey, bexaey, bexcey, cexbey, cexdey, dexcey, dexaey, aexdey;
   REAL aexcey, cexaey, bexdey, dexbey;
   REAL alift, blift, clift, dlift;
   REAL ab, bc, cd, da, ac, bd;
   REAL abc, bcd, cda, dab;
   REAL aezplus, bezplus, cezplus, dezplus;
   REAL aexbeyplus, bexaeyplus, bexceyplus, cexbeyplus;
   REAL cexdeyplus, dexceyplus, dexaeyplus, aexdeyplus;
   REAL aexceyplus, cexaeyplus, bexdeyplus, dexbeyplus;
   REAL det;
   REAL permanent, errbound;

   aex = pa[0] - pe[0];
   bex = pb[0] - pe[0];
   cex = pc[0] - pe[0];
   dex = pd[0] - pe[0];
   aey = pa[1] - pe[1];
   bey = pb[1] - pe[1];
   cey = pc[1] - pe[1];
   dey = pd[1] - pe[1];
   aez = pa[2] - pe[2];
   bez = pb[2] - pe[2];
   cez = pc[2] - pe[2];
   dez = pd[2] - pe[2];

   aexbey = aex * bey;
   bexaey = bex * aey;
   ab = aexbey - bexaey;
   bexcey = bex * cey;
   cexbey = cex * bey;
   bc = bexcey - cexbey;
   cexdey = cex * dey;
   dexcey = dex * cey;
   cd = cexdey - dexcey;
   dexaey = dex * aey;
   aexdey = aex * dey;
   da = dexaey - aexdey;

   aexcey = aex * cey;
   cexaey = cex * aey;
   ac = aexcey - cexaey;
   bexdey = bex * dey;
   dexbey = dex * bey;
   bd = bexdey - dexbey;

   abc = aez * bc - bez * ac + cez * ab;
   bcd = bez * cd - cez * bd + dez * bc;
   cda = cez * da + dez * ac + aez * cd;
   dab = dez * ab + aez * bd + bez * da;

   alift = aex * aex + aey * aey + aez * aez;
   blift = bex * bex + bey * bey + bez * bez;
   clift = cex * cex + cey * cey + cez * cez;
   dlift = dex * dex + dey * dey + dez * dez;

   det = (dlift * abc - clift * dab) + (blift * cda - alift * bcd);

   aezplus = Absolute(aez);
   bezplus = Absolute(bez);
   cezplus = Absolute(cez);
   dezplus = Absolute(dez);
   aexbeyplus = Absolute(aexbey);
   bexaeyplus = Absolute(bexaey);
   bexceyplus = Absolute(bexcey);
   cexbeyplus = Absolute(cexbey);
   cexdeyplus = Absolute(cexdey);
   dexceyplus = Absolute(dexcey);
   dexaeyplus = Absolute(dexaey);
   aexdeyplus = Absolute(aexdey);
   aexceyplus = Absolute(aexcey);
   cexaeyplus = Absolute(cexaey);
   bexdeyplus = Absolute(bexdey);
   dexbeyplus = Absolute(dexbey);
   permanent = ((cexdeyplus + dexceyplus) * bezplus
      + (dexbeyplus + bexdeyplus) * cezplus
      + (bexceyplus + cexbeyplus) * dezplus)
      * alift
      + ((dexaeyplus + aexdeyplus) * cezplus
      + (aexceyplus + cexaeyplus) * dezplus
      + (cexdeyplus + dexceyplus) * aezplus)
      * blift
      + ((aexbeyplus + bexaeyplus) * dezplus
      + (bexdeyplus + dexbeyplus) * aezplus
      + (dexaeyplus + aexdeyplus) * bezplus)
      * clift
      + ((bexceyplus + cexbeyplus) * aezplus
      + (cexaeyplus + aexceyplus) * bezplus
      + (aexbeyplus + bexaeyplus) * cezplus)
      * dlift;
   errbound = isperrboundA * permanent;
   if ((det > errbound) || (-det > errbound)) {
      return det;
   }

   return insphereadapt(pa, pb, pc, pd, pe, permanent);
}
